[GAP Forum] Sequence of equal words in FpGroups

[Костоусов Кирилл]

Hello,

Suppose I have the FpGroup G=<a,b| a^2=1, b^2=1>.
In this group a*b*a^2*b*a*b=a*b^2*a*b=a^2*b=b holds.

If I build this group in Gap:
gap>F:=FreeGroup("a", "b");
gap>AssignGeneratorVariables(F);
gap>G:=F/[a^2,b^2];
gap>AssignGeneratorVariables(G);
and ask if
gap>a*b^2*a*b=b
the Gap answers
gap>true

Can I obtain the whole sequence of equal words
a*b*a^2*b*a*b, a*b^2*a*b, a^2*b, b,
using Gap?

Kirill Kostousov