Dear Tim, you might have better luck with GAP's package ACE, perhaps it print out a sufficiently detailed trace of what it does during building and reducing the coset table. https://www.gap-system.org/Manuals/pkg/ace-5.2/htm/CHAP001.htm Also, on the webpage of one of the authors of ACE http://staff.itee.uq.edu.au/havas/ one can find
Proof Extraction After Coset Enumeration: PEACE version 1 Colin Ramsay's source code + some test scripts Another appoach might be to try a Knuth-Bendix rewriting on your presentation, perhaps it will be more illuminating. https://www.gap-system.org/Packages/kbmag.html (I don't know anything about this approach, whether it will work for this presentation or not, I have no idea) HTH Dima On Thu, Sep 19, 2019 at 03:14:59PM -0400, tk...@math.bu.edu wrote: > > 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 _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
