Dear Mrs. and Mr. Forum,
Peter Mueller writes
if I understand the documentation correctly, then a command like
should return the the group GL(2,2) as a permutation group (hopefully
in the natural representation, though that's not specified there).
He reports that in GAP3R4P2 this does not work.
The reason for this bug is that in spite of the promises in the manual
section 'The Basic Groups Library' nobody wrote the corresponding code.
The next upgrade will fix this, for general linear groups as well as for
special linear and symplectic groups, and general/special unitary groups.
For the moment, the following function should suffice.
GeneralLinearPermGroup := function( n, q )
local matgrp, # the desired group as matrix group
space, # natural vector space 'matgrp' acts on
vectors; # set of nonzero vectors in 'space'
matgrp:= GeneralLinearMatGroup( n, q );
vectors:= Elements( space );
RemoveSet( vectors, Zero( space ) );
return Operation( matgrp, vectors );