DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-04

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.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The Frattini subgroup of a profinite group is the intersection of its maximal proper closed subgroups

Definition

For a profinite group $G$ , the Frattini subgroup is

$Φ (G) : = ⋂ {M < M maximal proper closed subgroup of G} .$

The closure condition is part of the definition: in the profinite setting the maximal subgroups relevant to generation theory are maximal among proper closed subgroups, not arbitrary abstract subgroups.

Used by

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Gareth Wilkes, Profinite Groups and Group Cohomology lecture notes (standard reference, not scraped)
Alexander Lubotzky, Combinatorial group theory for pro-p groups (standard reference, not scraped)