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: reviewed
- Last edited by John Jones on 2019-05-23 20:24:01
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- columns.gps_groups.frattini_label
- columns.gps_groups.frattini_quotient
- group.rank
- lmfdb/groups/abstract/main.py (lines 427-429)
- lmfdb/groups/abstract/main.py (line 1885)
- lmfdb/groups/abstract/templates/abstract-show-group.html (line 297)
- lmfdb/groups/abstract/web_groups.py (line 723)
- lmfdb/groups/abstract/web_groups.py (line 2736)
- 2019-05-23 20:24:01 by John Jones (Reviewed)