Dear GAP-Forum,
On Thu, Nov 20, 2003 at 06:20:40PM +0000, Peter Campbell wrote:
> 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
in addtion, one gets
gap> FactorCosetAction(g,TrivialSubgroup(g));
[ f1, f2 ] -> [ (), () ]

Looks like a bug to me...
(that's with GAP  4.3fix5 of June, 2003, i686-pc-linux-gnu-gcc)

Dima

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