Dear Alexander,
Thank you very much for the explanation.
-Tim
On Thu, 19 Sep 2019, Hulpke,Alexander wrote:
> Dear GAP Forum,
>
> > On Sep 19, 2019, at 10:56 AM, tk...@math.bu.edu wrote:
> > I was looking at the finitely presented group
> >
> > G=<x,y | yx^3=x^2y; y^3x=xy^2>
> >
> > where one can show that G=[G,G], which is pretty easy.
> >
> > I had a nagging suspicion that it is actually trivial
> > and in GAP I found that this was the case:
> >
> > gap> f := FreeGroup( "x", "y" );;
> > gap> g := f / [ f.2*f.1^3*f.2^(-1)*f.1^(-2),f.2^3*f.1*f.2^(-2)*f.1^(-1) ];
> > gap> Size(g);
> > 1
> >
> > And I was able to work out that this was indeed the case by
> > playing with the relations.
> >
> > What I'm wondering is whether I can make GAP show me
> > how it determined this group was trivial?
>
> What GAP does is to try coset enumeration by a cyclic subgroup, and --
> assuming this enumeration terminates and returns the index -- rewrite the
> presentation to this cyclic subgroup, calculating the order of the subgroup
> then is easy.
>
> There is no mechanism provided to extract a proof from this. You would have
> to interface rather seriously with the coset enumeration (i.e. basically
> rewrite the routine) to extract an actual proof.
> You might want to look at
>
> http://dx.doi.org/doi:10.1017/S0004972700018529
>
> for a description on how this could be done (it is not implemented in GAP).
>
> Best,
>
> Alexander Hulpke
>
> -- Colorado State University, Department of Mathematics,
> Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
> email: hul...@colostate.edu
> http://www.math.colostate.edu/~hulpke
>
>
>
_______________________________________________
Forum mailing list
Forum@gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
