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If $G$ is a group, then the Frattini subgroup of $G$, denoted $\Phi(G)$, is the intersection of all maximal subgroups of $G$. If there are no maximal subgroups of $G$, then $\Phi(G)=G$.

The Frattini subgroup is always a characteristic subgroup, hence a normal subgroup, of $G$.

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• Review status: beta
• Last edited by John Jones on 2019-05-23 20:24:01
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