[GAP Forum] StructureDescription Revisited

[Robert F. Morse]

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