Question

let G be a group with operation . and let p,q be two elements of G. simplify p.q.q.q^-1.p^-1.q^-1 as much as possible.does answer change if G is ABELIAN?

Answer 1

p.q.(q.q^-1).p^-1.q^-1
p.q.p^-1.q^-1

If Abelian, the p.q=q.p and we can go on:

q.(p.p^-1).q^-1
q.q^-1
1

Answer 2

thanks steve SO DOES ANSWER CHANGE IF ABELIAN?