^ From:

> ^ Subject:

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

of PGL(2,q).

When I create the PGL by

gap> Pgl:=PGL(2,q);

it seems, that I get an isomorphic permutation group.

gap> P:=PGL(IsMatrixGroup,2,13);

seems not to work. Also, if I do something like

gap> G:=GL(2,13);

gap> c:=Center(Gl);

gap> P:=FactorGroup(Gl,c);

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,

Georg

> < [top]