[GAP Forum] Equal structure descriptions

[Stephen Linton]

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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