[GAP Forum] StructureDescription

[Nilo de Roock]

Hello Marco,

Thank you very much for your help.  And, yes I will use the support
address in the future for this sort of questions. Since GAP is Open
Source anyway, is it possible to subscribe to the support-list? These
lists usually become the best knowledgebase around, at least for the
other software I work with. ( The only thing that's preventing me from
reading the GAP source code is the language, C instead Java. Well,
Java wasn't around when it all started. )

Although I am still fairly new to GAP I think it's fair to say that
the feedback and answers on this list are both excellent and friendly.
Isn't that' a rather unique combination in the field?

kind regards,
nilo de roock

2006/2/26, Marco Costantini <costanti at science.unitn.it>:
> Dear Nilo de Roock,
>
> (Warning:
> this answer is a draft, and has not yet been discussed with other people
> of the GAP Support Group. More detailed information may (or may not)
> arrive later. Feel free to write again if you need more help. For any
> remark concerning this mail, please do not reply to me, but write to
> support at gap-system.org .)
>
> We offer to react as well as we can to questions, requests for help with
> problems, or complaints that you may have. However, for the sake of the whole
> user community of GAP, we ask you to separate these into two different
> categories.
>
> GAP Support.  We would like to deal with those topics that are more or less
> local to you, that is, are likely not of interest to most of the other GAP
> users by direct correspondence with you. Please send letters about such local
> problems and questions also to the address support at gap-system.org.
>
> GAP Forum.  On the other hand, the GAP Forum should be reserved for
> discussions about problems that are likely to interest many of the GAP users.
> It would also be welcome if you could occasionally tell other users in the
> GAP Forum about interesting applications you have made of GAP.
>
>
> On Sunday 26 February 2006 11:44, Nilo de Roock wrote:
> > Hello GAP forum,
> >
> > Forgive for yet another question (...) on this command, perhaps I am using
> > the wrong command for my purpose. When I execute the following command.
> >
> > gap> List(AllGroups(20),StructureDescription);
> >
> > GAP responds with
> > [ "C5 : C4", "C20", "C5 : C4", "D20", "C10 x C2" ]
> >
> > The issue I have here is that "C5:C4" occurs twice in the list.
>
> Yes, in fact StructureDescription is not injective, an two of the groups with
> 20 elements have a similar structure.
>
> > What I am
> > looking for is a command that would recognize that the Frobenius group
> > <s,t; s^4 = t^5 = 1, ts = st^2> is in there somewhere.
> >
> >
> > Even if I do...
> >
> > gap> F:=FreeGroup(2);
> > <free group on the generators [ f1, f2 ]>
> > gap> s:=F.1;
> > f1
> > gap> t:=F.2;
> > f2
> > gap> G:=F/[s^4,t^5,t*s*t^-2*s^-1];
> > <fp group on the generators [ f1, f2 ]>
> > gap> Size(G);
> > 20
> > gap> str(G);
> > "C5 : C4"
> > gap>
> >
> > the answer is "C5:C4".
> >
> >
> > I am getting lost on this command, and thus on GAP. Please help.
>
> A possibility is simply
>
> gap> IdGroup(G);
> [ 20, 3 ]
>
> that is, G is the 3rd group in AllGroups(20) .
>
> Another possibility is to use StructureDescription only to restrict to some of
> the groups, and then to proceed with something else. For instance
>
> gap> G_20_1 := SmallGroup(20,1);
> <pc group of size 20 with 3 generators>
> gap> G_20_3 := SmallGroup(20,3);
> <pc group of size 20 with 3 generators>
>
> After using StructureDescription you know that the other groups with 20
> elements are not isomorphic to your G.
>
> After that you can use:
>
> gap> IsomorphismGroups( G_20_1, G );
> fail
> gap> IsomorphismGroups( G_20_3, G );
> [ f1, f2, f3 ] -> [ f1^5, f1^2, f2 ]
>
> you can also use:
>
> gap> Length( ConjugacyClasses( G ) );
> 5
> gap> Length( ConjugacyClasses( G_20_1 ) );
> 8
> gap> Length( ConjugacyClasses( G_20_3 ) );
> 5
>
> you can also use anything else analogous.
>
> All the best,
> Marco Costantini
>