[GAP Forum] Re: A Possible bug in FGA

[Christian Sievers]

Laurent Bartholdi wrote:

> Hello world,
> Unless I'm terribly mistaken there's a problem with the FGA package:
> 
> GAP4, Version: 4.4.6 of 02-Sep-2005, i686-pc-linux-gnu-gcc
> gap> RequirePackage("FGA");
> true
> gap> F := FreeGroup(2);
> <free group on the generators [ f1, f2 ]>
> ### the identity automorphism
> gap> x := GroupHomomorphismByImages(F,F,GeneratorsOfGroup(F),GeneratorsOfGroup(F));
> [ f1, f2 ] -> [ f1, f2 ]
> gap> IsOne(x);
> ### and GAP freezes.

GAP uses a very general method which does not work for infinite groups,
and the FGA package implements no special method.

You can use this one:

  InstallMethod( IsOne,
     "for group general mappings with images",
     [ IsGroupHomomorphism and HasMappingGeneratorsImages ],
     hom -> IsEndoMapping( hom ) and MappingGeneratorsImages( hom )[ 1 ] =
                                     MappingGeneratorsImages( hom )[ 2 ]
  );

(As a workaround, you may prefer  x=IdentityMapping(F).)

To the developers:
I guess something like the above method should go somewhere to the
gap library as it is not free group specific.


All the best
Christian Sievers