[GAP Forum] trivializing a group

[Stephan Rosebrock]

Did you try:

Size(G);

That should, if it is the trivial group, give you the answer "1".
If it isn't, it will not stop running. Since it is not decidable
whether a presentation presents the trivial group there is not
more you can hope for.

Best wishes
Stephan Rosebrock



Am Sa, 15.08.2009, 19:15, schrieb Daniel Ruberman:
> 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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*  Dr. Stephan Rosebrock                                *
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