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I have been having trouble using GroupHomomorphismByImages, which seems

to take a very long time in a fairly straightforward situation. Here is

an example:

g:=Group((1,2,3,4,5,6),(1,2)); R:=[]; for k in [1..2] do M:=NullMat(6,6,GF(3)); for i in [1..6] do j:=i^g.generators[k]; M[i][j]:=Z(3)^0; od; R[k]:=M; od; GroupHomomorphismByImages(g,GeneralLinearGroup(6,3),g.generators,R);

This piece of code sets up a pair of matrices R{1] and R[2] which represent

the permutation action of the two generators of the symmetric group of

degree 6 on the natural permutation representation. Everything except the

last line takes hardly any time. The final line then takes some minutes

to run.

Evidently GroupHomomorphismByImages is doing a lengthy computation, but

by looking at the manual I can't tell what it is. From looking at

interrupt messages it appears to be computing a stablizer chain. I can think

of several things it might be doing that would take rather a long time, but

am not sure which is actually taking place.

Could you please shed some light on this situation?

My main aim is to set up a record which stores some of the information

in GroupHomomorphismByImages, but I don't necessarily need all this

information. Is there any way to bypass the computation that

GroupHomomorphismByImages is doing?

I am running version 3.2 of GAP without any of the subsequent patches.

With thanks for your help,

Luis Valero

valero@math.umn.edu

School of Mathematics, University of Minnesota, Minneapolis MN 55455

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