GAP

Main Branches

Downloads  Installation  Overview  Data Libraries  Packages  Documentation  Contacts  FAQ  GAP 3 

238 publications using GAP in the category "Associative rings and algebras"

[A08] Abdollahi, A., Commuting graphs of full matrix rings over finite fields, Linear Algebra Appl., 428 (11-12) (2008), 2947–2954.

[AJ19] Abdollahi, A. and Jafari, F., Zero divisor and unit elements with supports of size 4 in group algebras of torsion-free groups, Comm. Algebra, 47 (1) (2019), 424–449.

[AJ20] Abdollahi, A. and Jafari, F., Cardinality of product sets in torsion-free groups and applications in group algebras, J. Algebra Appl., 19 (4) (2020), 2050079, 24.

[AT18] Abdollahi, A. and Taheri, Z., Zero divisors and units with small supports in group algebras of torsion-free groups, Comm. Algebra, 46 (2) (2018), 887–925.

[A01] Aichinger, E., On the maximal ideals of non-zero-symmetric near-rings and of composition algebras of polynomial functions of $\Omega$-groups, Quaest. Math., 24 (4) (2001), 453–480.

[A02] Aichinger, E., The polynomial functions on certain semidirect products of groups, Acta Sci. Math. (Szeged), 68 (1-2) (2002), 63–81.

[AF04] Aichinger, E. and Farag, M., On when the multiplicative center of a near-ring is a subnear-ring, Aequationes Math., 68 (1-2) (2004), 46–59.

[AKS08] Aleev, R. Z., Kargapolov, A. V., and Sokolov, V. V., The ranks of central unit groups of integral group rings of alternating groups, Fundam. Prikl. Mat., 14 (7) (2008), 15–21.

[AS09] Aleev, R. Z. and Sokolov, V. V., On central unit groups of integral group rings of alternating groups, Proc. Steklov Inst. Math., 267 (suppl. 1) (2009), S1–S9.

[AA+21] Ali, S., Azad, H., Biswas, I., and de Graaf, W. A., A constructive method for decomposing real representations, J. Symbolic Comput., 104 (2021), 328–342.

[A00] Alp, M., Some results on derivation groups, Turkish J. Math., 24 (2) (2000), 121–128.

[A02] Alp, M., Enumeration of Whitehead groups of low order, Internat. J. Algebra Comput., 12 (5) (2002), 645–658.

[AA+14] Andruskiewitsch, N., Angiono, I., García Iglesias, A., Masuoka, A., and Vay, C., Lifting via cocycle deformation, J. Pure Appl. Algebra, 218 (4) (2014), 684–703.

[AF07] Andruskiewitsch, N. and Fantino, F., On pointed Hopf algebras associated with alternating and dihedral groups, Rev. Un. Mat. Argentina, 48 (3) (2007), 57–71 (2008).

[AF+10] Andruskiewitsch, N., Fantino, F., García, G. A., and Vendramin, L., On twisted homogeneous racks of type D, Rev. Un. Mat. Argentina, 51 (2) (2010), 1–16.

[AF+11] Andruskiewitsch, N., Fantino, F., García, G. A., and Vendramin, L., On Nichols algebras associated to simple racks, in Groups, algebras and applications, Amer. Math. Soc., Providence, RI, Contemp. Math., 537 (2011), 31–56.

[AF+10] Andruskiewitsch, N., Fantino, F., Graña, M., and Vendramin, L., Pointed Hopf algebras over some sporadic simple groups, C. R. Math. Acad. Sci. Paris, 348 (11-12) (2010), 605–608.

[AF+11] Andruskiewitsch, N., Fantino, F., Graña, M., and Vendramin, L., Finite-dimensional pointed Hopf algebras with alternating groups are trivial, Ann. Mat. Pura Appl. (4), 190 (2) (2011), 225–245.

[AF+11] Andruskiewitsch, N., Fantino, F., Graña, M., and Vendramin, L., Pointed Hopf algebras over the sporadic simple groups, J. Algebra, 325 (2011), 305–320.

[AF+11] Andruskiewitsch, N., Fantino, F., Graña, M., and Vendramin, L., The logbook of pointed Hopf algebras over the sporadic simple groups, J. Algebra, 325 (2011), 282–304.

[AGM17] Andruskiewitsch, N., Galindo, C., and Müller, M., Examples of finite-dimensional Hopf algebras with the dual Chevalley property, Publ. Mat., 61 (2) (2017), 445–474.

[AG19] Angiono, I. and García Iglesias, A., Liftings of Nichols algebras of diagonal type II: all liftings are cocycle deformations, Selecta Math. (N.S.), 25 (1) (2019), Paper No. 5, 95.

[AS20] Angiono, I. and Sanmarco, G., Pointed Hopf algebras over non abelian groups with decomposable braidings, I, J. Algebra, 549 (2020), 78–111.

[AKS04] Araújo, I. M., Kelarev, A. V., and Solomon, A., An algorithm for commutative semigroup algebras which are principal ideal rings, Comm. Algebra, 32 (4) (2004), 1237–1254.

[A21] Ardito, C. G., Morita equivalence classes of blocks with elementary abelian defect groups of order 32, J. Algebra, 573 (2021), 297–335.

[APS19] Ariki, S., Park, E., and Speyer, L., Specht modules for quiver Hecke algebras of type $C$, Publ. Res. Inst. Math. Sci., 55 (3) (2019), 565–626.

[B18] Bächle, A., Integral group rings of solvable groups with trivial central units, Forum Math., 30 (4) (2018), 845–855.

[BC17] Bächle, A. and Caicedo, M., On the prime graph question for almost simple groups with an alternating socle, Internat. J. Algebra Comput., 27 (3) (2017), 333–347.

[BH+18] Bächle, A., Herman, A., Konovalov, A., Margolis, L., and Singh, G., The status of the Zassenhaus conjecture for small groups, Exp. Math., 27 (4) (2018), 431–436.

[BK11] Bächle, A. and Kimmerle, W., On torsion subgroups in integral group rings of finite groups, J. Algebra, 326 (2011), 34–46.

[BKS20] Bächle, A., Kimmerle, W., and Serrano, M., On the first Zassenhaus conjecture and direct products, Canad. J. Math., 72 (3) (2020), 602–624.

[BM17] Bächle, A. and Margolis, L., On the prime graph question for integral group rings of 4-primary groups I, Internat. J. Algebra Comput., 27 (6) (2017), 731–767.

[BM17] Bächle, A. and Margolis, L., Rational conjugacy of torsion units in integral group rings of non-solvable groups, Proc. Edinb. Math. Soc. (2), 60 (4) (2017), 813–830.

[BM19] Bächle, A. and Margolis, L., An application of blocks to torsion units in group rings, Proc. Amer. Math. Soc., 147 (10) (2019), 4221–4231.

[BM19] Bächle, A. and Margolis, L., On the prime graph question for integral group rings of 4-primary groups II, Algebr. Represent. Theory, 22 (2) (2019), 437–457.

[BK07] Bagiński, C. and Konovalov, A., The modular isomorphism problem for finite $p$-groups with a cyclic subgroup of index $p^2$, in Groups St. Andrews 2005. Vol. 1, Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 339 (2007), 186–193.

[BK19] Bagiński, C. and Kurdics, J., The modular group algebras of $p$-groups of maximal class II, Comm. Algebra, 47 (2) (2019), 761–771.

[BK19] Bakshi, G. K. and Kaur, G., Semisimple finite group algebra of a generalized strongly monomial group, Finite Fields Appl., 60 (2019), 101571, 20.

[BP12] Balagović, M. and Policastro, C., Category $\scr O$ for the rational Cherednik algebra associated to the complex reflection group $G_12$, J. Pure Appl. Algebra, 216 (4) (2012), 857–875.

[BCJ19] Ballester-Bolinches, A., Cosme-Llópez, E., and Jiménez-Seral, P., Some contributions to the theory of transformation monoids, J. Algebra, 522 (2019), 31–60.

[B07] Balogh, Z., Further results on a filtered multiplicative basis of group algebras, Math. Commun., 12 (2) (2007), 229–238.

[BB20] Balogh, Z. and Bovdi, V., The isomorphism problem of unitary subgroups of modular group algebras, Publ. Math. Debrecen, 97 (1-2) (2020), 27–39.

[BJ11] Balogh, Z. and Juhász, T., Nilpotency class of symmetric units of group algebras, Publ. Math. Debrecen, 79 (1-2) (2011), 171–180.

[BL07] Balogh, Z. and Li, Y., On the derived length of the group of units of a group algebra, J. Algebra Appl., 6 (6) (2007), 991–999.

[BNY20] Bardakov, V. G., Neshchadim, M. V., and Yadav, M. K., Computing skew left braces of small orders, Internat. J. Algebra Comput., 30 (4) (2020), 839–851.

[B06] Bartholdi, L., Branch rings, thinned rings, tree enveloping rings, Israel J. Math., 154 (2006), 93–139.

[BN+20] Bendel, C. P., Nakano, D. K., Pillen, C., and Sobaje, P., Counterexamples to the tilting and $(p,r)$-filtration conjectures, J. Reine Angew. Math., 767 (2020), 193–202.

[BM05] Benini, A. and Morini, F., Partially balanced incomplete block designs from weakly divisible nearrings, Discrete Math., 301 (1) (2005), 34–45.

[BGK10] Bilgin, T., Gorentas, N., and Kelebek, I. G., Characterization of central units of $\Bbb ZA_n$, J. Korean Math. Soc., 47 (6) (2010), 1239–1252.

[BM01] Binder, F. and Mayr, P., Algorithms for finite near-rings and their $N$-groups, J. Symbolic Comput., 32 (1-2) (2001), 23–38
(Computer algebra and mechanized reasoning (St. Andrews, 2000)).

[B01] Blanchard, P. F., Exceptional group ring automorphisms for groups of order 96, Comm. Algebra, 29 (11) (2001), 4823–4830.

[B08] Bocklandt, R., Graded Calabi Yau algebras of dimension 3, J. Pure Appl. Algebra, 212 (1) (2008), 14–32.

[BK+21] Bonatto, M., Kinyon, M., Stanovský, D., and Vojtěchovský, P., Involutive latin solutions of the Yang-Baxter equation, J. Algebra, 565 (2021), 128–159.

[B18] Bonnafé, C., On the Calogero-Moser space associated with dihedral groups, Ann. Math. Blaise Pascal, 25 (2) (2018), 265–298.

[BZ17] Bouc, S. and Zimmermann, A., On a question of Rickard on tensor products of stably equivalent algebras, Exp. Math., 26 (1) (2017), 31–44.

[BE00] Bovdi, A. and Erdei, L., Unitary units in modular group algebras of $2$-groups, Comm. Algebra, 28 (2) (2000), 625–630.

[B12] Bovdi, V., Group rings in which the group of units is hyperbolic, J. Group Theory, 15 (2) (2012), 227–235.

[BJK11] Bovdi, V. A., Jespers, E., and Konovalov, A. B., Torsion units in integral group rings of Janko simple groups, Math. Comp., 80 (273) (2011), 593–615.

[BK08] Bovdi, V. A. and Konovalov, A. B., Integral group ring of the Mathieu simple group $M_23$, Comm. Algebra, 36 (7) (2008), 2670–2680.

[BK09] Bovdi, V. A. and Konovalov, A. B., Integral group ring of Rudvalis simple group, Ukraïn. Mat. Zh., 61 (1) (2009), 3–13.

[BK10] Bovdi, V. A. and Konovalov, A. B., Torsion units in integral group ring of Higman-Sims simple group, Studia Sci. Math. Hungar., 47 (1) (2010), 1–11.

[BKL08] Bovdi, V. A., Konovalov, A. B., and Linton, S., Torsion units in integral group ring of the Mathieu simple group $\rm M_22$, LMS J. Comput. Math., 11 (2008), 28–39.

[BKL11] Bovdi, V. A., Konovalov, A. B., and Linton, S., Torsion units in integral group rings of Conway simple groups, Internat. J. Algebra Comput., 21 (4) (2011), 615–634.

[BKS07] Bovdi, V. A., Konovalov, A. B., and Siciliano, S., Integral group ring of the Mathieu simple group $M_12$, Rend. Circ. Mat. Palermo (2), 56 (1) (2007), 125–136.

[BBM20] Bovdi, V., Breuer, T., and Maróti, A., Finite simple groups with short Galois orbits on conjugacy classes, J. Algebra, 544 (2020), 151–169.

[BH08] Bovdi, V. and Hertweck, M., Zassenhaus conjecture for central extensions of $S_5$, J. Group Theory, 11 (1) (2008), 63–74.

[BHK04] Bovdi, V., Höfert, C., and Kimmerle, W., On the first Zassenhaus conjecture for integral group rings, Publ. Math. Debrecen, 65 (3-4) (2004), 291–303.

[BK07] Bovdi, V. and Konovalov, A., Integral group ring of the first Mathieu simple group, in Groups St. Andrews 2005. Vol. 1, Cambridge Univ. Press, Cambridge, London Math. Soc. Lecture Note Ser., 339 (2007), 237–245.

[BK12] Bovdi, V. and Konovalov, A., Integral group ring of the Mathieu simple group $M_24$, J. Algebra Appl., 11 (1) (2012), 1250016, 10.

[BS18] Bovdi, V. and Salim, M., Group algebras whose groups of normalized units have exponent 4, Czechoslovak Math. J., 68(143) (1) (2018), 141–148.

[BW16] Boykett, T. and Wendt, G., Units in near-rings, Comm. Algebra, 44 (4) (2016), 1478–1495.

[BH+20] Breuer, T., Héthelyi, L., Horváth, E., and Külshammer, B., The Loewy structure of certain fixpoint algebras, Part I, J. Algebra, 558 (2020), 199–220.

[BH+06] Breuer, T., Héthelyi, L., Horváth, E., Külshammer, B., and Murray, J., Cartan invariants and central ideals of group algebras, J. Algebra, 296 (1) (2006), 177–195.

[BP06] Broche Cristo, O. and Polcino Milies, C., Central idempotents in group algebras, in Groups, rings and algebras, Amer. Math. Soc., Providence, RI, Contemp. Math., 420 (2006), 75–87.

[BJR09] Broche, O., Jespers, E., and Ruiz, M., Antisymmetric elements in group rings with an orientation morphism, Forum Math., 21 (3) (2009), 427–454.

[BW15] Brooksbank, P. A. and Wilson, J. B., The module isomorphism problem reconsidered, J. Algebra, 421 (2015), 541–559.

[CCD20] Campedel, E., Caranti, A., and Del Corso, I., Hopf-Galois structures on extensions of degree $p^2q$ and skew braces of order $p^2 q$: the cyclic Sylow $p$-subgroup case, J. Algebra, 556 (2020), 1165–1210.

[CM06] Carlson, J. F. and Matthews, G., Generators and relations for matrix algebras, J. Algebra, 300 (1) (2006), 134–159.

[CC99] Carnahan, S. and Childs, L., Counting Hopf Galois structures on non-abelian Galois field extensions, J. Algebra, 218 (1) (1999), 81–92.

[CH04] Chen, H. and Hiss, G., Projective summands in tensor products of simple modules of finite dimensional Hopf algebras, Comm. Algebra, 32 (11) (2004), 4247–4264.

[CH12] Chen, H. and Hiss, G., Notes on the Drinfeld double of finite-dimensional group algebras, Algebra Colloq., 19 (3) (2012), 483–492.

[CH+10] Chu, H., Hu, S., Kang, M., and Kunyavskii, B. E., Noether's problem and the unramified Brauer group for groups of order 64, Int. Math. Res. Not. IMRN (12) (2010), 2329–2366.

[CGW05] Cohen, A. M., Gijsbers, D. A. H., and Wales, D. B., BMW algebras of simply laced type, J. Algebra, 286 (1) (2005), 107–153.

[CGW14] Cohen, A. M., Gijsbers, D. A. H., and Wales, D. B., The Birman-Murakami-Wenzl algebras of type $D_n$, Comm. Algebra, 42 (1) (2014), 22–55.

[CW11] Cohen, A. M. and Wales, D. B., The Birman-Murakami-Wenzl algebras of type $\bold E_n$, Transform. Groups, 16 (3) (2011), 681–715.

[CZ13] Coquereaux, R. and Zuber, J., Drinfeld doubles for finite subgroups of $\rm SU(2)$ and $\rm SU(3)$ Lie groups, SIGMA Symmetry Integrability Geom. Methods Appl., 9 (2013), Paper 039, 36.

[CG11] Creedon, L. and Gildea, J., The structure of the unit group of the group algebra $\Bbb F_2^kD_8$, Canad. Math. Bull., 54 (2) (2011), 237–243.

[CH19] Creedon, L. and Hughes, K., Derivations on group algebras with coding theory applications, Finite Fields Appl., 56 (2019), 247–265.

[DEM13] Danz, S., Ellers, H., and Murray, J., The centralizer of a subgroup in a group algebra, Proc. Edinb. Math. Soc. (2), 56 (1) (2013), 49–56.

[D18] De Graaf, W. A., Classification of nilpotent associative algebras of small dimension, Internat. J. Algebra Comput., 28 (1) (2018), 133–161.

[KDP11] de Klerk, E., Dobre, C., and Pasechnik, D. V., Numerical block diagonalization of matrix $\ast$-algebras with application to semidefinite programming, Math. Program., 129 (1, Ser. B) (2011), 91–111.

[M20] de Mendonça, L. A., Weak commutativity and nilpotency, J. Algebra, 564 (2020), 276–299.

[RRZ11] del Río, Á., Ruiz Marín, M., and Zalesskii, P., Subgroup separability in integral group rings, J. Algebra, 347 (2011), 60–68.

[DS14] Devadas, S. and Sam, S. V., Representations of rational Cherednik algebras of $G(m,r,n)$ in positive characteristic, J. Commut. Algebra, 6 (4) (2014), 525–559.

[D07] Ðoković, D. Ž., Poincaré series of some pure and mixed trace algebras of two generic matrices, J. Algebra, 309 (2) (2007), 654–671.

[DZ17] Dokuchaev, M. and Zalesski, A., On the automorphism group of rational group algebras of finite groups, in Groups, rings, group rings, and Hopf algebras, Amer. Math. Soc., Providence, RI, Contemp. Math., 688 (2017), 33–51.

[DNV15] Dong, J., Natale, S., and Vendramin, L., Frobenius property for fusion categories of small integral dimension, J. Algebra Appl., 14 (2) (2015), 1550011, 17.

[DJK10] Dooms, A., Jespers, E., and Konovalov, A., From Farey symbols to generators for subgroups of finite index in integral group rings of finite groups, J. K-Theory, 6 (2) (2010), 263–283.

[DG+18] Dougherty, S. T., Gildea, J., Taylor, R., and Tylyshchak, A., Group rings, $G$-codes and constructions of self-dual and formally self-dual codes, Des. Codes Cryptogr., 86 (9) (2018), 2115–2138.

[DZ10] Dzhumadilʹdaev, A. and Zusmanovich, P., Commutative 2-cocycles on Lie algebras, J. Algebra, 324 (4) (2010), 732–748.

[E08] Eick, B., Computing automorphism groups and testing isomorphisms for modular group algebras, J. Algebra, 320 (11) (2008), 3895–3910.

[E11] Eick, B., Computing nilpotent quotients of associative algebras and algebras satisfying a polynomial identity, Internat. J. Algebra Comput., 21 (8) (2011), 1339–1355.

[EK16] Eick, B. and King, S., The isomorphism problem for graded algebras and its application to $\rm mod$-$p$ cohomology rings of small $p$-groups, J. Algebra, 452 (2016), 487–501.

[EM17] Eick, B. and Moede, T., Coclass theory for finite nilpotent associative algebras: algorithms and a periodicity conjecture, Exp. Math., 26 (3) (2017), 267–274.

[EW18] Eick, B. and Wesche, M., Enumeration of nilpotent associative algebras of class 2 over arbitrary finite fields, J. Algebra, 503 (2018), 573–589.

[EKV15] Eisele, F., Kiefer, A., and Van Gelder, I., Describing units of integral group rings up to commensurability, J. Pure Appl. Algebra, 219 (7) (2015), 2901–2916.

[EG+08] Estrada, S., García-Rozas, J. R., Peralta, J., and Sánchez-García, E., Group convolutional codes, Adv. Math. Commun., 2 (1) (2008), 83–94.

[FV13] Fantino, F. and Vendramin, L., On twisted conjugacy classes of type D in sporadic simple groups, in Hopf algebras and tensor categories, Amer. Math. Soc., Providence, RI, Contemp. Math., 585 (2013), 247–259.

[FK15] Ferraz, R. A. and Kitani, P. M., Units of $\Bbb ZC_p^n$, Comm. Algebra, 43 (11) (2015), 4936–4950.

[FW11] Fong, Y. and Wang, C. -., On derivations of centralizer near-rings, Taiwanese J. Math., 15 (4) (2011), 1437–1446.

[FGV07] Freyre, S., Graña, M., and Vendramin, L., On Nichols algebras over $\rm SL(2,\Bbb F_q)$ and $\rm GL(2,\Bbb F_q)$, J. Math. Phys., 48 (12) (2007), 123513, 11.

[FGV10] Freyre, S., Graña, M., and Vendramin, L., On Nichols algebras over $\rm PGL(2,q)$ and $\rm PSL(2,q)$, J. Algebra Appl., 9 (2) (2010), 195–208.

[GR21] Gaddis, J. and Rogalski, D., Quivers supporting twisted Calabi-Yau algebras, J. Pure Appl. Algebra, 225 (9) (2021), 106645, 33.

[GG17] García Iglesias, A. and Giraldi, J. M. J., Liftings of Nichols algebras of diagonal type III. Cartan type $G_2$, J. Algebra, 478 (2017), 506–568.

[GM11] García Iglesias, A. and Mombelli, M., Representations of the category of modules over pointed Hopf algebras over $\Bbb S_3$ and $\Bbb S_4$, Pacific J. Math., 252 (2) (2011), 343–378.

[GP21] García Iglesias, A. and Pacheco Rodríguez, E., Examples of liftings of modular and unidentified type: $\germufo(7,8)$ and $\germbr(2,a)$, J. Algebra Appl., 20 (1) (2021), 2140002, 17.

[GV14] García Iglesias, A. and Vay, C., Finite-dimensional pointed or copointed Hopf algebras over affine racks, J. Algebra, 397 (2014), 379–406.

[GV18] García Iglesias, A. and Vay, C., Copointed Hopf algebras over $\BbbS_4$, J. Pure Appl. Algebra, 222 (9) (2018), 2784–2809.

[GLO21] García-Sánchez, P. A., Llena, D., and Ojeda, I., Critical binomial ideals of Northcott type, J. Aust. Math. Soc., 110 (1) (2021), 48–70.

[GS10] Gilbert, N. D. and Samman, M., Endomorphism seminear-rings of Brandt semigroups, Comm. Algebra, 38 (11) (2010), 4028–4041.

[G10] Gildea, J., The structure of the unit group of the group algebra of Pauli's group over any field of characteristic 2, Internat. J. Algebra Comput., 20 (5) (2010), 721–729.

[G13] Gildea, J., Zassenhaus conjecture for integral group ring of simple linear groups, J. Algebra Appl., 12 (6) (2013), 1350016, 10.

[G16] Gildea, J., Torsion units for a Ree group, Tits group and a Steinberg triality group, Rend. Circ. Mat. Palermo (2), 65 (1) (2016), 139–157.

[GO16] Gildea, J. and O'Brien, K., Torsion unit for some untwisted exceptional groups of Lie type, Acta Sci. Math. (Szeged), 82 (3-4) (2016), 451–466.

[GT16] Gildea, J. and Tylyshchak, A., Torsion units in the integral group ring of $\rm PSL(3, 4)$, J. Algebra Appl., 15 (1) (2016), 1650013, 9.

[GD11] Gonçalves, J. Z. and Del Río, Á., Bass cyclic units as factors in a free group in integral group ring units, Internat. J. Algebra Comput., 21 (4) (2011), 531–545.

[GGR14] Gonçalves, J. Z., Guralnick, R. M., and del Río, Á., Bass units as free factors in integral group rings of simple groups, J. Algebra, 404 (2014), 100–123.

[G11] Grabowski, J. E., Braided enveloping algebras associated to quantum parabolic subalgebras, Comm. Algebra, 39 (10) (2011), 3491–3514.

[GHV11] Graña, M., Heckenberger, I., and Vendramin, L., Nichols algebras of group type with many quadratic relations, Adv. Math., 227 (5) (2011), 1956–1989.

[GHS00] Green, E. L., Heath, L. S., and Struble, C. A., Constructing endomorphism rings via duals, in Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), ACM, New York (2000), 129–136.

[GHS01] Green, E. L., Heath, L. S., and Struble, C. A., Constructing homomorphism spaces and endomorphism rings, J. Symbolic Comput., 32 (1-2) (2001), 101–117
(Computer algebra and mechanized reasoning (St. Andrews, 2000)).

[GNS15] Grishkov, A., Nunes, R., and Sidki, S., On groups with cubic polynomial conditions, J. Algebra, 437 (2015), 344–364.

[GS10] Grundman, H. G. and Smith, T. L., Galois realizability of groups of order 64, Cent. Eur. J. Math., 8 (5) (2010), 846–854.

[GM19] Gupta, S. and Maheshwary, S., Finite semisimple group algebra of a normally monomial group, Internat. J. Algebra Comput., 29 (1) (2019), 159–177.

[HLV12] Heckenberger, I., Lochmann, A., and Vendramin, L., Braided racks, Hurwitz actions and Nichols algebras with many cubic relations, Transform. Groups, 17 (1) (2012), 157–194.

[HP08] Henke, A. and Paget, R., Brauer algebras with parameter $n=2$ acting on tensor space, Algebr. Represent. Theory, 11 (6) (2008), 545–575.

[HS15] Herman, A. and Singh, G., Revisiting the Zassenhaus conjecture on torsion units for the integral group rings of small groups, Proc. Indian Acad. Sci. Math. Sci., 125 (2) (2015), 167–172.

[H07] Hertweck, M., A note on the modular group algebras of odd $p$-groups of $M$-length three, Publ. Math. Debrecen, 71 (1-2) (2007), 83–93.

[H08] Hertweck, M., Zassenhaus conjecture for $A_6$, Proc. Indian Acad. Sci. Math. Sci., 118 (2) (2008), 189–195.

[HN04] Hertweck, M. and Nebe, G., On group ring automorphisms, Algebr. Represent. Theory, 7 (2) (2004), 189–210.

[HS06] Hertweck, M. and Soriano, M., On the modular isomorphism problem: groups of order $2^6$, in Groups, rings and algebras, Amer. Math. Soc., Providence, RI, Contemp. Math., 420 (2006), 177–213.

[HS07] Hertweck, M. and Soriano, M., Parametrization of central Frattini extensions and isomorphisms of small group rings, Israel J. Math., 157 (2007), 63–102.

[HSL98] Héthelyi, L., Szőke, M., and Lux, K., The restriction of indecomposable modules of group algebras and the quasi-Green correspondence, Comm. Algebra, 26 (1) (1998), 83–95.

[HM14] Hille, L. and Müller, J., On tensor products of path algebras of type $A$, Linear Algebra Appl., 448 (2014), 222–244.

[HK00] Hiss, G. and Kessar, R., Scopes reduction and Morita equivalence classes of blocks in finite classical groups, J. Algebra, 230 (2) (2000), 378–423.

[HKN12] Hiss, G., Koenig, S., and Naehrig, N., On the socle of an endomorphism algebra, J. Pure Appl. Algebra, 216 (6) (2012), 1288–1294.

[H16] Hoshi, A., Birational classification of fields of invariants for groups of order 128, J. Algebra, 445 (2016), 394–432.

[IMM14] Iovanov, M., Mason, G., and Montgomery, S., $FSZ$-groups and Frobenius-Schur indicators of quantum doubles, Math. Res. Lett., 21 (4) (2014), 757–779.

[IL00] Ivanyos, G. and Lux, K., Treating the exceptional cases of the MeatAxe, Experiment. Math., 9 (3) (2000), 373–381.

[JS20] Jensen, B. T. and Su, X., Existence of Richardson elements for seaweed Lie algebras of finite type, J. Lond. Math. Soc. (2), 101 (2) (2020), 505–529.

[JRV14] Jespers, E., del Río, Á., and Van Gelder, I., Writing units of integral group rings of finite abelian groups as a product of Bass units, Math. Comp., 83 (285) (2014), 461–473.

[JO+13] Jespers, E., Olteanu, G., del Río, Á., and Van Gelder, I., Group rings of finite strongly monomial groups: central units and primitive idempotents, J. Algebra, 387 (2013), 99–116.

[K10] Kawai, H., Construction of maximal ideals of commutative group algebras, Internat. J. Algebra Comput., 20 (3) (2010), 381–389.

[K15] Keilberg, M., Automorphisms of the doubles of purely non-abelian finite groups, Algebr. Represent. Theory, 18 (5) (2015), 1267–1297.

[K18] Keilberg, M., Examples of non-$FSZ$ $p$-groups for primes greater than three, Proc. Amer. Math. Soc., 146 (1) (2018), 85–92.

[K19] Keilberg, M., Some behaviors of $FSZ$ groups under central products, central quotients, and regular wreath products, J. Algebra, 529 (2019), 89–113.

[K19] Keilberg, M., The FSZ properties of sporadic simple groups, J. Algebra Appl., 18 (1) (2019), 1950016, 32.

[K20] Keilberg, M., Correction to: Automorphisms of the doubles of purely non-abelian finite groups, Algebr. Represent. Theory, 23 (3) (2020), 1237–1241.

[K06] Kimmerle, W., On the prime graph of the unit group of integral group rings of finite groups, in Groups, rings and algebras, Amer. Math. Soc., Providence, RI, Contemp. Math., 420 (2006), 215–228.

[K13] Kimmerle, W., Unit groups of integral group rings: old and new, Jahresber. Dtsch. Math.-Ver., 115 (2) (2013), 101–112.

[KK17] Kimmerle, W. and Konovalov, A., On the Gruenberg-Kegel graph of integral group rings of finite groups, Internat. J. Algebra Comput., 27 (6) (2017), 619–631.

[KK+19] Koch, A., Kohl, T., Truman, P. J., and Underwood, R., Normality and short exact sequences of Hopf-Galois structures, Comm. Algebra, 47 (5) (2019), 2086–2101.

[KPS13] Kochetov, M., Parsons, N., and Sadov, S., Counting fine grading on matrix algebras and on classical simple Lie algebras, Internat. J. Algebra Comput., 23 (7) (2013), 1755–1781.

[K07] Kohl, T., Groups of order $4p$, twisted wreath products and Hopf-Galois theory, J. Algebra, 314 (1) (2007), 42–74.

[K13] Kohl, T., Regular permutation groups of order $mp$ and Hopf Galois structures, Algebra Number Theory, 7 (9) (2013), 2203–2240.

[K07] Konovalov, A., Wreath products in modular group algebras of some finite 2-groups, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 23 (2) (2007), 125–127.

[KK07] Konovalov, A. and Krivokhata, A., On the isomorphism problem for unit groups of modular group algebras, Acta Sci. Math. (Szeged), 73 (1-2) (2007), 53–59.

[KT04] Konovalov, A. B. and Tsapok, A. G., Symmetric subgroups of a normalized multiplicative group of the modular group algebra of a finite $p$-group, Nauk. V\=isn. Uzhgorod. Univ. Ser. Mat. \=Inform. (9) (2004), 20–24.

[K04] Künzer, M., On representations of twisted group rings, J. Group Theory, 7 (2) (2004), 197–229.

[KKG17] Kukharev, A. V., Kaĭgorodov, I. B., and Gorshkov, I. B., When the group ring of a simple finite group is semiserial, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 460 (Voprosy Teorii PredstavleniĭAlgebr i Grupp. 32) (2017), 168–189.

[KP15] Kukharev, A. V. and Puninskiĭ, G. E., Semiserial group rings of finite groups. Sporadic simple groups and Suzuki groups, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 435 (Voprosy Teorii PredstavleniĭAlgebr i Grupp. 28) (2015), 73–94.

[LL09] La Scala, R. and Levandovskyy, V., Letterplace ideals and non-commutative Gröbner bases, J. Symbolic Comput., 44 (10) (2009), 1374–1393.

[LS18] Ladisch, F. and Schürmann, A., Equivalence of lattice orbit polytopes, SIAM J. Appl. Algebra Geom., 2 (2) (2018), 259–280.

[LS17] Landrock, P. and Sambale, B., On centers of blocks with one simple module, J. Algebra, 472 (2017), 339–368.

[LLS21] Lénárt, S., Lőrinczi, Á., and Szöllősi, I., Tree representations of the quiver $\tilde\Bbb E_6$, Colloq. Math., 164 (2) (2021), 221–250.

[LS14] Levandovskyy, V. and Shepler, A. V., Quantum Drinfeld Hecke algebras, Canad. J. Math., 66 (4) (2014), 874–901.

[LBP06] Li, Y., Bell, H. E., and Phipps, C., On reversible group rings, Bull. Austral. Math. Soc., 74 (1) (2006), 139–142.

[L13] Liu, S., Brauer algebras of type $\rm F_4$, Indag. Math. (N.S.), 24 (2) (2013), 428–442.

[LZZ17] Liu, Y., Zhou, G., and Zimmermann, A., Stable equivalences of Morita type do not preserve tensor products and trivial extensions of algebras, Proc. Amer. Math. Soc., 145 (5) (2017), 1881–1890.

[L01] Lorenz, M., Multiplicative invariants and semigroup algebras, Algebr. Represent. Theory, 4 (3) (2001), 293–304.

[LMR94] Lux, K., Müller, J., and Ringe, M., Peakword condensation and submodule lattices: an application of the MEAT-AXE, J. Symbolic Comput., 17 (6) (1994), 529–544.

[M19] Margolis, L., On the prime graph question for integral group rings of Conway simple groups, J. Symbolic Comput., 95 (2019), 162–176.

[MR18] Margolis, L. and del Río, Á., An algorithm to construct candidates to counterexamples to the Zassenhaus Conjecture, J. Algebra, 514 (2018), 536–558.

[MR19] Margolis, L. and del Río, Á., Partial augmentations power property: a Zassenhaus conjecture related problem, J. Pure Appl. Algebra, 223 (9) (2019), 4089–4101.

[MS18] Margolis, L. and Schnabel, O., Twisted group ring isomorphism problem, Q. J. Math., 69 (4) (2018), 1195–1219.

[MS20] Margolis, L. and Schnabel, O., The twisted group ring isomorphism problem over fields, Israel J. Math., 238 (1) (2020), 209–242.

[MT18] Markov, V. T. and Tuganbaev, A. A., Centrally essential group algebras, J. Algebra, 512 (2018), 109–118.

[ME04] Martin, P. P. and Elgamal, A., Ramified partition algebras, Math. Z., 246 (3) (2004), 473–500.

[MS18] Maxson, C. J. and Saxinger, F., Rings of congruence preserving functions, Monatsh. Math., 187 (3) (2018), 531–542.

[MM02] Mayr, P. and Morini, F., Nearrings whose set of $N$-subgroups is linearly ordered, Results Math., 42 (3-4) (2002), 339–348.

[M02] Meyer, H., Konjugationsklassensummen in endlichen Gruppenringen, Bayreuth. Math. Schr. (66) (2002), viii+160
(Dissertation, Universität Bayreuth, Bayreuth, 2002).

[M06] Meyer, H., On a subalgebra of the centre of a group ring, J. Algebra, 295 (1) (2006), 293–302.

[M08] Meyer, H., On a subalgebra of the centre of a group ring. II, Arch. Math. (Basel), 90 (2) (2008), 112–122.

[M03] Müller, J., A note on applications of the `Vector Enumerator' algorithm, Linear Algebra Appl., 365 (2003), 291–300
(Special issue on linear algebra methods in representation theory).

[NT20] Naves, F. A. and Talpo, H. L., Minimum degree of an $A$-identity of $E\otimes E$, Internat. J. Algebra Comput., 30 (6) (2020), 1237–1256.

[OR03] Olivieri, A. and del Río, Á., An algorithm to compute the primitive central idempotents and the Wedderburn decomposition of a rational group algebra, J. Symbolic Comput., 35 (6) (2003), 673–687.

[ORS04] Olivieri, A., del Río, Á., and Simón, J. J., On monomial characters and central idempotents of rational group algebras, Comm. Algebra, 32 (4) (2004), 1531–1550.

[O07] Olteanu, G., Computing the Wedderburn decomposition of group algebras by the Brauer-Witt theorem, Math. Comp., 76 (258) (2007), 1073–1087.

[OR07] Olteanu, G. and del Río, Á., Group algebras of Kleinian type and groups of units, J. Algebra, 318 (2) (2007), 856–870.

[OR09] Olteanu, G. and del Río, Á., An algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package \tt wedderga, J. Symbolic Comput., 44 (5) (2009), 507–516.

[OV15] Olteanu, G. and Van Gelder, I., Construction of minimal non-abelian left group codes, Des. Codes Cryptogr., 75 (3) (2015), 359–373.

[P19] Pascoe, J. E., An elementary method to compute the algebra generated by some given matrices and its dimension, Linear Algebra Appl., 571 (2019), 132–142.

[P20] Pérennou, H., Polynomiality of projective modular representations graded rings, J. Algebra, 541 (2020), 308–323.

[P09] Peterson, G. L., The idempotent quiver of a nearring, Algebra Colloq., 16 (3) (2009), 463–478.

[PS13] Peterson, G. L. and Scott, S. D., Units of compatible nearrings, III, Monatsh. Math., 171 (1) (2013), 103–124.

[P09] Pfeiffer, G., A quiver presentation for Solomon's descent algebra, Adv. Math., 220 (5) (2009), 1428–1465.

[P19] Posur, S., Constructing equivariant vector bundles via the BGG correspondence, J. Symbolic Comput., 91 (2019), 57–73.

[P21] Posur, S., A constructive approach to Freyd categories, Appl. Categ. Structures, 29 (1) (2021), 171–211.

[Q13] Quadrat, A., Grade filtration of linear functional systems, Acta Appl. Math., 127 (2013), 27–86.

[RW18] Reich, D. J. and Walton, C., Explicit representations of 3-dimensional Sklyanin algebras associated to a point of order 2, Involve, 11 (4) (2018), 585–608.

[RS10] Reiner, V. and Stamate, D. I., Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals, Adv. Math., 224 (6) (2010), 2312–2345.

[R00] Rossmanith, R., Lie centre-by-metabelian group algebras in even characteristic. I, II, Israel J. Math., 115 (2000), 51–75, 77–99.

[R18] Ryabov, G. K., On the separability of Schur rings over abelian $p$-groups, Algebra Logika, 57 (1) (2018), 73–101.

[SS18] Sahai, M. and Sharan, B., On Lie nilpotent modular group algebras, Comm. Algebra, 46 (3) (2018), 1199–1206.

[S20] Sakurai, T., Central elements of the Jennings basis and certain Morita invariants, J. Algebra Appl., 19 (8) (2020), 2050160, 13.

[S07] Salim, M. A. M., Torsion units in the integral group ring of the alternating group of degree 6, Comm. Algebra, 35 (12) (2007), 4198–4204.

[S92] Sandling, R., Presentations for unit groups of modular group algebras of groups of order $16$, Math. Comp., 59 (200) (1992), 689–701.

[S16] Schauenburg, P., Computing higher Frobenius-Schur indicators in fusion categories constructed from inclusions of finite groups, Pacific J. Math., 280 (1) (2016), 177–201.

[S17] Schönnenbeck, S., Resolutions for unit groups of orders, J. Homotopy Relat. Struct., 12 (4) (2017), 837–852.

[S01] Seidel, U., Exceptional sequences for quivers of Dynkin type, Comm. Algebra, 29 (3) (2001), 1373–1386.

[S09] Sidki, S. N., Functionally recursive rings of matrices—two examples, J. Algebra, 322 (12) (2009), 4408–4429.

[S01] Swallow, J. R., Quadratic descent for quaternion algebras, Comm. Algebra, 29 (10) (2001), 4523–4544.

[SS15] Szántó, C. and Szöllősi, I., Hall polynomials and the Gabriel-Roiter submodules of simple homogeneous modules, Bull. Lond. Math. Soc., 47 (2) (2015), 206–216.

[SS17] Szántó, C. and Szöllősi, I., A short solution to the subpencil problem involving only column minimal indices, Linear Algebra Appl., 517 (2017), 99–119.

[SS21] Szántó, C. and Szöllősi, I., Schofield sequences in the Euclidean case, J. Pure Appl. Algebra, 225 (5) (2021), 106586, 123.

[S14] Szöllősi, I., Computing the extensions of preinjective and preprojective Kronecker modules, J. Algebra, 408 (2014), 205–221.

[T14] Thiel, U., A counter-example to Martino's conjecture about generic Calogero-Moser families, Algebr. Represent. Theory, 17 (5) (2014), 1323–1348.

[T15] Thiel, U., Champ: a Cherednik algebra Magma package, LMS J. Comput. Math., 18 (1) (2015), 266–307.

[T17] Timmer, J., Indicators of bismash products from exact symmetric group factorizations, Comm. Algebra, 45 (10) (2017), 4444–4465.

[U95] Ufnarovskij, V. A., Combinatorial and asymptotic methods in algebra [ MR1060321 (92h:16024)], in Algebra, VI, Springer, Berlin, Encyclopaedia Math. Sci., 57 (1995), 1–196.

[VO11] Van Gelder, I. and Olteanu, G., Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents, Finite Fields Appl., 17 (2) (2011), 157–165.

[VY19] Vojtěchovský, P. and Yang, S. Y., Enumeration of racks and quandles up to isomorphism, Math. Comp., 88 (319) (2019), 2523–2540.

[WWY19] Walton, C., Wang, X., and Yakimov, M., Poisson geometry of PI three-dimensional Sklyanin algebras, Proc. Lond. Math. Soc. (3), 118 (6) (2019), 1471–1500.

[WZ19] Walton, C. and Zhang, J. J., On the quadratic dual of the Fomin-Kirillov algebras, Trans. Amer. Math. Soc., 372 (6) (2019), 3921–3945.

[W10] Wendt, G., Minimal left ideals of near-rings, Acta Math. Hungar., 127 (1-2) (2010), 52–63.

[Y05] Yoshikawa, M., The intersection of normal closed subsets of an association scheme is not always normal, J. Fac. Sci. Shinshu Univ., 40 (2005), 37–40 (2006).

[Z13] Zelikson, S., On crystal operators in Lusztig's parametrizations and string cone defining inequalities, Glasg. Math. J., 55 (1) (2013), 177–200.

[Z18] Zimmermann, A., Külshammer ideals of algebras of quaternion type, J. Algebra Appl., 17 (8) (2018), 1850157, 26.