Category:Maximal Normal Subgroups
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This category contains results about Maximal Normal Subgroups.
Definitions specific to this category can be found in Definitions/Maximal Normal Subgroups.
Let $G$ be a group.
Let $N \le G$ be a proper normal subgroup.
Then $N$ is a maximal normal subgroup of $G$ if and only if:
- For every normal subgroup $M$ of $G$, $N \subseteq M \subseteq G$ implies $N = M$ or $M = G$.
That is, if and only if there is no normal subgroup of $G$, except $N$ and $G$ itself, which contains $N$.
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