Dear Daniel, did you try coset enumeration? It would eventually terminate if the index is finite, although one cannot give a bound on how long it will run... Usually it works fast, though... See Coset Tables and Coset Enumeration _____________ Finitely Presented Groups in the manual.
Hope this helps, Dmitrii On Sun, Aug 16, 2009 at 01:15:17AM +0800, Daniel Ruberman wrote: > Does anyone have any practical advice on showing that a finite > presentation that one suspects to be for the trivial group, in fact is > the trivial group? The initial presentation of the group (G below) > has 8 generators and 18 relations of total length 88. After applying > the commands > gap> P:=PresentationFpGroup(G); > <presentation with 8 gens and 18 rels of total length 88> > gap> TzGoGo(P); > #I there are 4 generators and 14 relators of total length 183 > #I there are 4 generators and 14 relators of total length 181 > > there doesn't seem to be much simplification! > > Obvious tests, such as AbelianInvariants(G) or running > LowIndexSubgroupsFpGroup(G,8); > don't distinguish G from the trivial group. > > Any suggestions would be gratefully accepted; this could of course > include calculations doable in GAP or otherwise. > > Thanks, > Daniel Ruberman > > Department of Mathematics > Brandeis University > Waltham, MA 02454 > http://www.brandeis.edu/~ruberman/ > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
