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On Tue, 3 Sep 1996, Norai Romeu Rocco wrote:

> I haven't been able to understand the following situation in the coset > enumeration: > > Given, for instance, the finitely presented (finite) group g, > > gap> F:=FreeGroup("a", "b");; > gap> > gap> g:=F/[F.1^4, F.2^4, Comm(F.1, F.2)^F.1/Comm(F.1, F.2^(-1)), > Comm(F.1, F.2)^F.2/Comm(F.1^(-1), F.2), > Comm(F.1^2, F.2)/Comm(F.1, F.2^(-1))*Comm(F.1, F.2)]; > Group( a, b ) > gap> > > then GAP computes its Size quickly: > > gap> Index(g, TrivialSubgroup(g)); > 128 > > Now observe that the last relator comes from the commutator identity > > [x^2, y] = [x, y]^x*[x, y] > > which should give the last relator as a consequence of the third one > > [F.1^2, F.2] = [F.1, F.2^(-1)]*[F.1, F.2] > ............... > Could anyone tell me what's wrong? Seems to be a small bug in coset > enumaration (?). > NO --- User error: missing parentheses in

Comm(F.1^2, F.2)/Comm(F.1, F.2^(-1))*Comm(F.1, F.2)];

should be:

Comm(F.1^2, F.2)/ ( Comm(F.1, F.2^(-1))*Comm(F.1, F.2)] );

/ and = are not equivalent operators in presentations.

I think this explains it all.

George Havas (havas@cs.uq.edu.au) Phone: +61 7 3365 2904; Fax: +61 7 3365 1999 Department of Computer Science AUS http://www.cs.uq.oz.au/personal/havas The University of Queensland UK http://www-groups.dcs.st-and.ac.uk/~havas Queensland 4072 AUSTRALIA US http://dimacs.rutgers.edu/~havas

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