[GAP Forum] Constructing semilinear, outer linear, and affine groups

[Jan De Beule]

Dear Vipul Naik,

Currently, we are developing a share package for GAP, called "FinInG", of which a beta release is available through 

http://cage.ugent.be/geometry/fining.php

Almost everything you ask related to the projective groups, is available in the package. 

Feel free to contact us if you want the most recent version of the package. We plan to submit the package in the near future.

Best regards,

Jan De Beule

Op 4-jun-2012, om 16:34 heeft Vipul Naik het volgende geschreven:

> Dear GAP Forum,
> 
> I would appreciate if any of you could provide me code (or suggest a
> package) that would help construct these groups for a positive integer
> n and a prime power q of prime p. If I have the code, I should be able
> to tweak it to construct the variants. I am not too concerned about
> computational efficiency:
> 
> (1) General semilinear group Gamma L(n,q), defined as semidirect
> product with base GL(n,q) and acting group the automorphism group of
> F_q (i.e., the Galois group of F_q over F_p).
> 
> I'm also interested in constructing variants where the base group is
> taken as SL(n,q), PGL(n,q), or PSL(n,q), and also variants where we
> take a subgroup of the Galois group rather than the whole Galois group.
> 
> (2) Outer linear group OL(n,q), defined as the semidirect product of
> GL(n,q) by a cyclic group of order two where the non-identity element
> acts by the transpose-inverse map.
> 
> I also want to consider variants where the base group is taken as
> SL(n,q) instead of GL(n,q), as well as the variant where q = p^2 and
> we take the semidirect product by a cyclic group of order two acting
> by the conjugate-transpose-inverse.
> 
> (3) General affine group denoted GA(n,q) or AGL(n,q) defined as the
> semidirect product of the n-dimensional vector space over F_q by
> GL(n,q) with its natural action.
> 
> I also want to construct semidirect products for chosen subgroups of
> GL(n,q), and more generally, semidirect products associated with
> n-dimensional representations of groups over F_q.
> 
> Thank you!
> 
> Vipul
> 
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Jan De Beule                                          jdebeule at cage.ugent.be
Postdoctoraal onderzoeker FWO
Vakgroep Wiskunde
Krijgslaan 281, S22
B 9000 Gent (Belgium)                         http://cage.ugent.be/~jdebeule
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