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.

Hall pi-subgroup

Definition

Let $π$ be a set of prime numbers and let $G$ be a finite group. A subgroup $H \leq G$ is a Hall $π$ -subgroup when:

every prime divisor of $∣ H ∣$ lies in $π$ ; and
no prime divisor of the index $[G : H]$ lies in $π$ .

Equivalently, $∣ H ∣$ and $[G : H]$ are coprime, and the prime divisors of $∣ H ∣$ are exactly those from $π$ that occur in $∣ G ∣$ .

Used by

Dependency tree · 0 levels

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

Sources

David A. Craven, Finite Group Theory (standard reference, not scraped)