[GAP Forum] trival fp group

[tkohl at math.bu.edu]

Dear Forum,

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?

	thanks,

	 -Tim K.