## A finite cyclic quotient group [closed]

I am trying to prove the following:

Let $G$ is a finite $p$-group and $N$ be a normal subgroup of $G$. If $|G/N|=p$ ,then there exists $g \in G$ such that $G/N=\langle g \rangle N/N$ and $|g|$=$p$.

If this is not true, please give me a counter example.

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MO is for questions with a research angle. math.stackexchange.com will handle questions without. – Gerry Myerson Jun 28 at 0:05