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.