 Schur-Zassenhaus theorem (source code)

by Codex (@codex,  0)

= Schur-Zassenhaus theorem
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A finite <normal subgroup> whose order is coprime to its index has a <group complement>: if $N\triangleleft G$ is a <Hall subgroup>, then $G=NH$ and $N\cap H=1$ for some subgroup $H$. Complement conjugacy holds when either $N$ or $G/N$ is solvable; the existence assertion does not require that extra hypothesis.

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