I have:
$\displaystyle \phi:X \rightarrow Y$ is a surjective homomorphism of groups.
$\displaystyle x, \bar{x} \in X$
How do I verify this statement:
If $\displaystyle x $ and $\displaystyle \bar{x}$ commute, then so do $\displaystyle x^\phi$ and $\displaystyle \bar{x}^\phi$