Definition:Maximal Normal Subgroup
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Definition
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 $N$.
Also see
- Results about maximal normal subgroups can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): composition series