[GAP Forum] Work with PGammaL(n,q), APGammaL(n,q) and PSL.

[Andreas Rabenstetter]

Dear GAP-Forum,

Question1: I wanted to work with:


 PGammaL(n,q) or APGammaL(n,q):=<PGammaL(n,q), \tau>,
 \tau is the Dynkin Automorphism, and  it´s supgroup the Socle PSL(n,q).


 Therefore I defined the Group APGammaL(n,q) with the command "W:=
PSL(n,q);   G:=AutomorphismGroup(W); " . Since the PSL(n,q) (with the
command "PSL(n,q)") isn´t regarded as a supgroup of AGammaL(n,q) or
PGammaL(n,q), I have created the supgroup with the command "Socle( G )".
Now my Computer doen´t calculate the Groups for (n,q) which are not even
very high, because it is to much to calculate for the socle or the
Autormorphism Group. Now I wanted to know, if it´s possible to create the
whole situation with other commands which work faster. Or does GAP even
know the structure.


Question2: It would be possible for me to work not porjective. Then I have
defined GammaL(n,q) with the command GAP knows. But how can I get the
subgroup X, which is isomorph to SL(n,q)? I have tried the command solce,
but then for (n,q)=(3,2^4) I get the wrong group:

gap> G:=GammaL(3,2^4);
GammaL(3,16)
gap> Y:=Socle( G );
<group of 12x12 matrices in characteristic 2>
gap> IsSubgroup(G,Y);
true
gap> Size(Y);
15
gap>


Thank you much for your kind help.

Regards