Source: wikibot/frattini-subgroup
= Frattini subgroup
{wiki=Frattini_subgroup}
The Frattini subgroup is an important concept in group theory, particularly in the study of finite groups. It is defined as the subgroup of a group \\( G \\) that is generated by all the non-generators of \\( G \\). Specifically, it has a few equivalent characterizations: 1. **Definition**: The Frattini subgroup \\( \\Phi(G) \\) of a group \\( G \\) is the intersection of all maximal subgroups of \\( G \\).