I need to prove that if $G$ is a group, $M$ is a maximal subgroup of $G$ and $Z(G) \nsubseteq M$,then $M \unlhd G$. Is true that $G = Z(G)M$, right? Is this enough?
2026-03-25 17:21:42.1774459302
Let $G$ be a finite group and $M$ be a maximal subgroup of $G$. If $G = Z(G)M$, then $M$ is normal in $G$
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