Frattini subgroup of a group $G$ is the intersection of all maximal proper subgroups of $G$. It can be also equivalently defined as the set of all nongenerators of $G$ ($x \in G$ is a nongenerator of $G$ iff $\forall S \subset G ((\langle S \cup {x} \rangle = G) \rightarrow (\langle S \rangle = G))$). Frattini subgroup is always a characteristic subgroup. To be used with the tag [group-theory].
Frattini subgroup of a group $G$ is the intersection of all maximal proper subgroups of $G$. It can be also equivalently defined as the set of all nongenerators of $G$ ($x \in G$ is a nongenerator of $G$ iff $\forall S \subset G ((\langle S \cup \{x\} \rangle = G) \rightarrow (\langle S \rangle = G))$). Frattini subgroup is always a characteristic subgroup. To be used with the tag group-theory.
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