Let $\displaystyle A$ be a group with subset $\displaystyle H=\langle h \rangle \times C$ where $\displaystyle h$ has infinite order and $\displaystyle C$ is finite central subgroup in $\displaystyle A$.

Suppose $\displaystyle A$ is $\displaystyle \langle h \rangle$-potent.

Can $\displaystyle A/C$ be $\displaystyle \langle h \rangle$-potent?