[GAP Forum] trivializing a group

[Dima Pasechnik]

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/
> 
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