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

[Bill Allombert]

On Wed, Mar 25, 2009 at 12:43:20AM +0800, Asst. Prof. Dmitrii (Dima) Pasechnik wrote:
> 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)

However it is certainly possible to represent PGL(K,n) and PSL(K,n) as a matrix
group in GL(K,n^2) as the image of the action of GL(K,n) on End(K^n) by
conjugacy and identifying End(K^n) with K^(n^2).

This should be easily done in GAP.

Cheers,
Bill.