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While running a program the following "silly" presentation was discovered: < a,b | a^2*b*a^-1, b*a^2*b^-1, a^-3 >.

This presentation obviously defines the trivial group.

GAP calculates the order of the group defined by this presentation to be

3, as the following illustrates:

gap> f:=FreeGroup(2);; gap> a:=f.1;; b:=f.2;; gap> g:=f/[a^2*b*a^(-1), b*a^2*b^(-1), a^(-3)];; gap> Size(g); 3

Can anyone help?

Peter Campbell.

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