Solution
= Solution
\b[Can be false.] Take the <Klein four-group> $G=C_2\times C_2$ and $H=C_2\times\{e\}$. It is a <normal subgroup> because $G$ is an <abelian group>. Both $H$ and $G/H$ have order two and are <cyclic groups>. But every nonidentity element of $G$ has order two, so none generates its four elements. Thus $G$ is not cyclic.