I am trying to use GAP to establish equality of two words in a finitely
presented group and am having problems.
First here is a successful test case:
f:=FreeGroup(5);;
rel:=[(f.(5)*f.(1))^5];;
g:=f/rel;;
u:=GeneratorsOfGroup(g);;
(u[5]*u[1])^5 = Identity(g); #testing this identity which is actually a
given relation works successfully
true
But if I add some more relators to rel, I cannot even get
equality to the identity of the first relator. Here's what I tried:
f:=FreeGroup(5);;
rel:=[(f.(5)*f.(1))^5];;
for i in [1..4] do
Add(rel,(f.(i)*f.(i+1))*(f.(5)*f.(1))^(-1));
od;
rel;;
g:=f/rel;;
u:=GeneratorsOfGroup(g);
(u[5]*u[1])^5 = Identity(g); #I gave up waiting for an answer
Why is this so difficult?
What I really want in this group is to show that
u[1]^5*u[2]*u[4]*u[1]*u[3]*u[5] = Identity(g)
Any help would be appreciated.
--Edwin Clark
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