[GAP Forum] IsConjugatorIsomorphism for A5

[Alexander Hulpke]

Dear Forum, Dear Andreas Baechle,

> I encountered some (at least for me) unexpected behavior of the command IsConjugatorIsomorphism.
> 
> gap> g := RestrictedMapping(f, S);
> GeneralRestrictedMapping( ^(), Group([ (2,4)(3,5), (2,3)(4,5) ]), A5 )
> gap> IsConjugatorIsomorphism(g);
> false
> 

What happens is that the test for permutation groups (as a relic from an older, more restrictive definition) tests the map for `IsBijective’ which causes the rejection.
I will submit a fix (changing the test to be only for `IsInjective’) for inclusion in future releases.

Regards,

  Alexander Hulpke


> When I run this with other groups from the SmallGroup library everything seems to work and I get the expected output "true".
> 
> My first guess was that G (or S) is / are of a data type conflicting with the natural embedding described in http://www.gap-system.org/Manuals/doc/ref/chap40.html#X7F31FECC7A3D4A8A  However
> 
> gap> IsPermGroup(G);
> true
> gap> IsPermGroup(S);
> true
> 
> When replacing G by an isomorphic fp-group (H := Image(IsomorphismFpGroup(G));) it works (but is quite slow).  Also with other simple / perfect groups the result is as expected.  What is so special about this case?  And is there a good workaround to make this work for all groups from the SmallGroup library?
> 
> Thanks in advance for any help,
>  Andreas Bächle
> 
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