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Dear GAP Forum,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]

However, removing the last relator one gets the presentation

gap> h:=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)]; Group( a, b ) gap>

and now,

gap> Index(h, TrivialSubgroup(h));

Error, the coset enumeration has defined more than 64000 cosets:

type 'return;' if you want to continue with a new limit of 128000 cosets,

type 'quit;' if you want to quit the coset enumeration,

type 'maxlimit := 0; return;' in order to continue without a limit,

in

CosetTableFpGroup( G, H ) called from

G.operations.Index( G, U ) called from

Index( h, TrivialSubgroup( h ) ) called from

main loop

brk> quit;

gap> quit;

Could anyone tell me what's wrong? Seems to be a small bug in coset

enumaration (?).Thanks in advance for any help.

Norai Rocco.

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