Dear GAP Forum, Alireza,
Here are a couple of GAP functions to construct SL(d,q):2 and PSL(d,q):2,
where the :2 is the graph (duality) automorphism. SL(d,q):2 is constructed
as a subgroup of GL(2d,q) geenrated by elements (in block form):
[ g 0 ] and [ 0 I ]
[ 0 g^-T ] [ I 0 ]
for g in SL(d,q).
Derek Holt.
SL2 := function(d,q)
sl := SL(d,q);
gsl := GeneratorsOfGroup(sl);
gens := [];
for g in gsl do
Add( gens,
MatrixByBlockMatrix(BlockMatrix([[1,1,g],[2,2,TransposedMat(g^-1)]],2,2)));
od;
i := IdentityMat(d,GF(q));
Add( gens,
MatrixByBlockMatrix(BlockMatrix([[1,2,i],[2,1,i]],2,2)) );
return Subgroup( GL(2*d,q), gens );
end;
PSL2 := function(d,q)
sl2 := SL2(d,q);
v := Concatenation([1], 0*[1..2*d-1]) * Z(q)^0;
return Action(sl2, Orbit(sl2,v,OnLines), OnLines);
end;
gap> c := ConjugacyClasses( PSL2(5,5) );;
gap> Length(c);
465
The conjugacy class computation took a couple of hours.
On Wed, Jul 26, 2006 at 01:39:12PM +0330, arashrafi wrote:
> Dear Pubbers,
>
> Thank you very much from Sven Reichard, Leonard and Scott Murray for
> responding to my last message. The reality is this fact that I need the
> conjecacy classes of the group PSL(5,5):2, but I know GAP library does
> not have this group. Is there any possibility for including such
> information on GAP?
>
> All the best, Alireza
> -----------------------------------
> Ali Reza Ashrafi,
> Professor of Mathematics
> Department of Mathematics,
> Faculty of Science,
> University of Kashan,
> Kashan,Iran.
>
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