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

Thanks in advance

Re: Non-abelian group question

Your proof is almost complete. You state that

Quote:

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 $\displaystyle z$ exists, namely $\displaystyle z=y^{-1}xy.$

Re: Non-abelian group question