Dear GAP Forum members,
this is probably a stupid question, but I'm only a poor engineer
without any strong mathematical background hardly understanding
what I am doing with group theory...
I want to use GAP(4r2) with grape to to construct a CayleyGraph
for the group PGL(2,q). My generators are a set of matrices of the
form [[a*Z(q)^0, b*Z(q)^0], [c*Z(q)^0, d*Z(q)^0]] which are Elements
When I create the PGL by
it seems, that I get an isomorphic permutation group.
seems not to work. Also, if I do something like
I get again an isomorphic permutation group.
Now my question: How can I find the proper homomorphism to convert
the generators from the form [[a*Z(q)^0, b*Z(q)^0], [c*Z(q)^0, d*Z(q)^0]]
to a form suitable for the isomorphic permutation group representation
that is used by GAP for the PGL in order to use them with the
CayleyGraph-Function from grape.
I would be very grateful if somebody could give me a hint, even if
this question seems to be very stupid.
Thanks in advance and best Regards,