Groups-order and commutativity

Reference no: EM13125686

1. If x is an element of a group and x is of order n then the elements 1, x, x^2,...x^n-1 are distinct (don't know how to show this!)

2. Let Y=<u,v/u^4=v^3=1, uv=v^2u^2> Y here is a group show

a) v^2=v^-1

b) v commutes with u^3

c) v commutes with u

d) uv=1

e) u=1, deduce that v=1 and conclude that Y=1

Reference no: EM13125686

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