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,

Φ(G)=G∩⋂MM

where M runs over all maximal subgroups of G. If G has no maximal subgroups then Φ(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.