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Probably I just don't understand this. But "Image" doesn't seem to be

working as the manual says it should.

I constructed GL(2,3) as a matrix group and got the permutation

representation f (operation homomorphism) of it acting on vectors

(including the zero vector -- on RowSpace(2,GF(3))). Then I tried

applying the homomorphism to a pre-defined matrix:

gap> m1; [ [ Z(3)^0, Z(3)^0 ], [ 0*Z(3), Z(3)^0 ] ] gap> Image(f,m1); Error, <E> must be a domain or a set in DomainOps.IsSubset( G, H ) called from D.operations.IsSubset( D, E ) called from IsSubset( arg[1].source, arg[2] ) called from Image( f, m1 ) called from main loop brk> quit; gap> m1^f; (4,5,6)(7,9,8) gap>

As you can see, the "^" form worked, but "Image" itself did not. And

why is it worrying about subsets when I'm trying to use the element

version of "Image"?

When I tried the set version I got the same error message:

gap> Image(f,[m1]);

Error, <E> must be a domain or a set in

DomainOps.IsSubset( G, H ) called from

D.operations.IsSubset( D, E ) called from

IsSubset( arg[1].source, arg[2] ) called from

Images( map, elm ) called from

fun( i ) called from

..

brk> quit;

gap>

So the set version of "Image" doesn't work here either. This is

especially mystifying, as the error message says [m1] is not a subset

of f.source. At least I think that's what it means. But it IS a subset

of f.source.

What am I doing wrong?

David Sibley

sibley@math.psu.edu

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