Dear Tim,
your presentation is a special case of a whole family considered in
C. F. Miller III and P. E. Schupp,
Some presentations of the trivial group. in: Groups, languages and
geometry (South Hadley, MA, 1998), 113–115,
Contemp. Math., 250, Amer. Math. Soc., Providence, RI, 1999.
Maybe you can extract some arguments from this paper.
Best wishes,
Benjamin
Am 19.09.19 um 18:56 schrieb tk...@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.
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