# Non-abelian group question

• Mar 30th 2012, 11:37 PM
Daniiel
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

• Mar 31st 2012, 12:00 AM
Sylvia104
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 $z$ exists, namely $z=y^{-1}xy.$
• Mar 31st 2012, 12:13 AM
Daniiel
Re: Non-abelian group question
Thanks very much Sylvia!