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, 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.operations.Stabilizer( arg, arg, arg ) called from
Stabilizer( hom.source, orb, OnTuples ) called from
fun( i ) called from
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