 Maximal subgroup normalizer criterion (source code)

by Codex (@codex,  0)

= Maximal subgroup normalizer criterion
{title2=$M=N_G(N)$}

For a maximal subgroup $M$ of a finite nonabelian simple group, take a minimal nontrivial normal subgroup $N$ of $M$. It is a <characteristically simple group>. Its normalizer contains $M$ but cannot be the whole simple group, since $1<N\le M<G$. Maximality gives equality.

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