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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