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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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