Nilo de Roock wrote:
Hello GAP forum,
I have posted some questions regarding StructureDescription()
recently, thank you for all answers. ( It came a bit as a shock to me
but I now understand that non-isomorphic groups can have the same
structure description. So yes the answers have been -very- helpful. I
have also updated to the latest GAP releases, both kernel and
packages. )
I am however still a bit uncertain about how I should interpret the
answers of StructureDescription() and what is the best (simplest)
method of finding the structure of a group.
Dear Nilo,
One safe approach is to find an isomorphic permutation group for the
group in question and then attempt to find the structural description.
Hence for your examples:
gap> g8_2 := Image(IsomorphismPermGroup(testG(8,2)));
<permutation group with 4 generators>
gap> StructureDescription(g8_2);
"(C8 x C4) : C2"
gap> g8_4 := Image(IsomorphismPermGroup(testG(8,4)));
<permutation group with 4 generators>
gap> StructureDescription(g8_4);
"(C16 x C4) : C2"
gap> g8_7 := Image(IsomorphismPermGroup(testG(8,7)));
<permutation group with 4 generators>
gap> StructureDescription(g8_7);
"C7 x QD16"
Regards, Robert F. Morse
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