# Math Help - Non-abelian group question

1. ## Non-abelian group question

To show that a non-abelian group has elements a,b and c such that xy = yz and x≠z,

Would this be the correct approach?

For some x, y in a non-abelian group G

xy≠yx

and if

xy = yz for some z in G

then x≠z otherwise

xy≠yx

Is not satisfied for elements x and y of the group.

Is more detail required?

I feel like it is too straight forward

2. ## Re: Non-abelian group question

Your proof is almost complete. You state that

Originally Posted by Daniiel
and if

xy = yz for some z in G

then x≠z otherwise

xy=yx
To complete the proof, you need to state that such an element $z$ exists, namely $z=y^{-1}xy.$

3. ## Re: Non-abelian group question

Thanks very much Sylvia!