[GAP Forum] trivializing a group

[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/