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Dear Gap-forum!

Reading the GAP 3.1 manual we were trying example at the bottom of the

page 91. The example reads as follows:

gap> A:=Z(3)*[[0,1],[1,0]];;B:=Z(3)*[[0,1],[-1,0]];; gap> G:=Group(A,B); Group( [ [ 0*Z(3), Z(3) ], [ Z(3), 0*Z(3) ] ], [ [ 0*Z(3), Z(3) ], [ Z(3)^0, 0*Z(3) ] ] ) gap> Size(G); 8 gap> G.name:="G"; "G" gap> d8:=Operation(G,Orbit(G,Z(3)*[1,0])); Group( (1,2)(3,4), (1,2,3,4) ) gap> e:=OperationHomomorphism(Subgroup(G,[B]),d8); OperationHomomorphism( Subgroup( G, [ [ [ 0*Z(3), Z(3) ], [ Z(3)^0, 0*Z(3) ] ] ] ), Group( (1,2)(3,4), (1,2,3,4) ) )

Uptill now things go well. But we don't understand the following

error message:

gap> Kernel(e);

Error, Record: element 'permDomain' must have an assigned value at

if not d in G.permDomain ... in

stb.operations.Stabilizer( stb, pnt, OnPoints ) called from

GroupOps.Stabilizer( G, d, opr ) called from

arg[1].operations.Stabilizer( arg[1], arg[2], arg[3] ) called from

Stabilizer( hom.source, orb, OnTuples ) called from

fun( i ) called from

..

brk>

The correct answer (according to the manual) is:

Subgroup( G, [ ] )

Maybe we are missing some library file?

As the example is just rewritten from the manual, it should work.

Similar problems occur on the "top example" of the page 94 (the

example deals with the same group G as the previuos one).

The problem is in the computing of images.

GAP computes Image (c, A), but not e.g Image(c, A*B) (the function

Image in this example seems to work only with generators A, B).

The problem seems to be due to the fact that the matrices are over

GF(3). The same things go well for the isomorfic group generated by

the same matrices, but over Q.

Jaroslav Gurican, Martin Skoviera

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