[GAP Forum] Equal structure descriptions

[R.E. Boss]

Thanks.
I should have consulted the manual first.

Still think it is strange that StructureDescription does not determine the group up to isomorphism.


R.E. Boss


> -----Oorspronkelijk bericht-----
> Van: Stephen Linton [mailto:sal at cs.st-andrews.ac.uk]
> Verzonden: maandag 20 augustus 2012 10:03
> Aan: R.E. Boss
> CC: forum at gap-system.org
> Onderwerp: Re: [GAP Forum] Equal structure descriptions
> 
> Dear GAP Forum,
> 
> R.E. Boss asked about non-isomorphic groups with equal structure descriptions.
> This CAN happen. The manual entry for "StructureDescription"
> 
> http://www.gap-system.org/Manuals/doc/ref/chap39.html#X8199B74B84446971
> 
> says:
> 
> "The   string  returned  by  StructureDescription  is  <not>  an  isomorphism
>   invariant:  non-isomorphic  groups  can  have the same string value, and two
>   isomorphic   groups  in  different  representations  can  produce  different
>   strings."
> 
> StructureDescription provides an "informal" overview of the structure of a group, which is a useful
> first view for small groups. More sophisticated function in the same area include  IdGroup;
> the StandardPresentation function of the anupq package and IsomorphismGroups, each of which is described
> in the appropriate manual.
> 
> 	Yours
> 
> 	Steve Linton
> 
> On 20 Aug 2012, at 08:00, R.E. Boss wrote:
> 
> > What can I conclude from the equal structure descriptions below I stumbled upon?
> >
> >
> >
> > R.E. Boss
> >
> >
> >
> >
> >
> > gap> StructureDescription(SmallGroup(64,156));
> >
> > "Q8 : Q8"
> >
> > gap> StructureDescription(SmallGroup(64,158));
> >
> > "Q8 : Q8"
> >
> >
> >
> > gap> StructureDescription(SmallGroup(64,155));
> >
> > "(C8 : C4) : C2"
> >
> > gap> StructureDescription(SmallGroup(64,157));
> >
> > "(C8 : C4) : C2"
> >
> > gap> StructureDescription(SmallGroup(64,159));
> >
> > "(C8 : C4) : C2"
> >
> >
> >
> > gap> StructureDescription(SmallGroup(64,160));
> >
> > "(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)"
> >
> > gap> StructureDescription(SmallGroup(64,179));
> >
> > "C8 : Q8"
> >
> > gap> StructureDescription(SmallGroup(64,180));
> >
> > "(C2 x C2) . (C2 x D8) = (C4 x C2) . (C2 x C2 x C2)"
> >
> >
> >
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