Frattini subgroup

	Main Article	Discussion	Related Articles  [?]	Bibliography  [?]	External Links  [?]	Citable Version  [?]
	This editable Main Article is under development and subject to a disclaimer. [edit intro]

In group theory, the Frattini subgroup is the intersection of all maximal subgroups of a group.

Formally,

${\displaystyle \Phi (G)=G\cap \bigcap _{M}M\,}$

where M runs over all maximal subgroups of G. If G has no maximal subgroups then ${\displaystyle \Phi (G)=G}$.

The Frattini is a subgroup, which is normal and indeed characteristic.

References[edit]

• Marshall Hall jr (1959). The theory of groups. New York: Macmillan, 156.