[GAP Forum] PSL(n,q) with matrix filter

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Andreas,

PSL is not a matrix group, it is an action of SL on the projective
space, i.e. on the 1-dimensional subspaces. It is the quotient of SL
over the centre, which consists of scalar matrices. Then indeed, when
q=2, it is isomorphic  to SL, so you can work with e.g.
SpecialLinearGroup( 2, 2 ) directly.
(You can certainly do this for bigger q too, but you have to keep in
mind that yoiu work with a preimage of the homomorphism)

HTH,
Dmitrii

2009/3/24 Andreas Rabenstetter <gletschereis at googlemail.com>:
> Dear gap-forum team.
> I´m interested in the PSL(n,q) and wanted it to represent it by matrix. Is
> it possible to gererate this  group in GAP with deal with matrices? I tied
> the out:
>
> ProjectiveSpecialLinearGroup( [IsMatrixGroup ], 2, 2 );
> and ProjectiveSpecialLinearGroup( IsMatrixGroup , 2, 2 );
>
> but it doesn´t work. The filter chosen when I let GAP fix it, is not such
> usable for me.
> Thank you very much .
>
> Regards
> Andreas Rabenstetter
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