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