Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17
How statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
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The Frattini subgroup as the intersection of the maximal subgroups of a finite group
Definition
For a finite group , the Frattini subgroup is If , the family is empty and its intersection inside is itself. Thus .
Depends on
Used by
- The Fitting and Frattini subgroups of S₃ Example
- The p-cores, Fitting subgroup, and Frattini subgroup of S₄ Example
- The Frattini subgroup consists exactly of the nongenerators of a finite group Lemma
- Nilpotence lifts over the Frattini subgroup of a finite group Theorem
- Sylow and maximal-subgroup characterizations of finite nilpotence Theorem
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 6 results over 6 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- David A. Craven, Finite Group Theory, Sections 1.4 and 2.3 (standard reference, not scraped)