Let Y=(u v/u^4=v^3=1,uv=u^2v^2)
b) v commutes with u^3
c)u commutes with u
e)show that u=1, deduce that v=1 and conclude that Y=1
(a) Since v^3=1, then v^(-1)*v^3=v^(-1), thus v^2=v^(-1)
(b) Since uv=u^2v^2, then u^(-1)uvv^(-1)=u^(-1)u^2v^2v^(-1), then 1=uv. So we get uv=1. Then v=u^(-1). Thus ...
Permutation Groups and Commutativity are investigated. The solution is detailed and well presented.