[GAP Forum] Subgroup of PcGroup

[Rashid Ali]

Dear GAP Forum

I am working on computation of self connected Transversals. In order to display elements of transversals in an order in powers of I used its PolyCyclic group. The groups that i am working on are 2-group [(2x2x2)x2]x7 of order 112, 3-group [(3x3)x3]x4 of order 108 and 4-group [(4x4x4)x4]x7 of order 1792. The problem is solved for 2-group by using following commands in GAP:
gap> F:=FreeGroup("b","u","v","w","z");;
gap> AssignGeneratorVariables(F);;
gap> rels:=[b^7,u^2,v^2,w^2,z^2,Comm(u,b)/(v*u),Comm(v,b)/(v*w),Comm(w,b)/(u*v*w),Comm(z,b),Comm(v,u),Comm(w,u),Comm(w,v),Comm(z,v),Comm(z,w)];;
gap> G:=F/rels;
<fp group on the generators [ b, u, v, w, z ]>
gap> OG:=Order(G);
112
gap> Gpol:=PcGroupFpGroup(G);
<pc group of size 112 with 5 generators>
gap> OGpol:=Order(Gpol);
112
gap> AssignGeneratorVariables(Gpol);
gap> Hpol:=Subgroup(Gpol,[u,v,w*z]);
Group([ u, v, w*z ])
gap> OH:=Order(Hpol);
8
And then I found 64 self-connected transversals and 256 H-connected transversals.

But when I used these commands for 3-group, the last command and all other command related to the subgroup of PcGroup G return an error message given bellow:

gap> F:=FreeGroup( "b","u","v", "z");;
gap> AssignGeneratorVariables(F);;
gap>relators:=[b^4,u^3,v^3,z^3,u^b*v, v^b/u, Comm(u,v),Comm(u,z),Comm(v,z),Comm(b,z)];;
gap> G:=F/relators;;
gap> OG:=Order(G);
108
gap> Gpoly:=PcGroupFpGroup(G);
<pc group of size 108 with 4 generators>
gap> AssignGeneratorVariables(Gpoly);;
gap> Hpoly:=Subgroup(Gpoly,[u,v*z]);
Group([ u, v*z ])
gap> OH:=Order(Hpoly);
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 2nd choice method found for `InducedPcgsByGeneratorsNC' on 2 argumen\
ts called from
InducedPcgsByGeneratorsNC( pcgs, gens ) called from
InducedPcgsByGenerators( pa, GeneratorsOfGroup( grp ) ) called from
Pcgs( grp ) called from
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop ...
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk>
Although GAP calculates order of the generators of subgroup H i.e. Order(u) = 3 and Order(v*z) =3, but it cannot calculate order of H.

Could you please help me how to resolve this problem or suggest me some other possibility for writing elements of the transversals in some systematic order for example in ascending positive powers of 'b'.

Thank You

Rashid Ali