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## Homework Statement

If x and g are elements of the group G, prove that |x|=|g

^{-1}xg|. Deduce that |ab| =|ba| for all a,b [itex]\in[/itex] G

## Homework Equations

## The Attempt at a Solution

I've written a proof but does not seem quite right:

if (g

^{-1}xg)

^{n}= x

^{m}then n must be equal m

g

^{-n}x

^{n}g

^{n}= x

^{m}then

x

^{n}g

^{n}=g

^{n}x

^{m}

x

^{n}=g

^{n}x

^{m}g

^{-n}

x

^{m}=g

^{-n}x

^{n}g

^{n}

x

^{n}= g

^{n}(g

^{-n}x

^{m}g

^{n})g

^{-n}

x

^{n}= x

^{m}

n = m