DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

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.

p-regular and p-singular elements

Let $G$ be a finite group and let $p$ be a prime.

An element $g \in G$ is $p$ -regular when $p ∤ ∣ g ∣$ , where $∣ g ∣$ denotes the order of $g$ . It is $p$ -singular when $p ∣ ∣ g ∣$ .

The set of $p$ -regular elements is written

$G^{0} : = {g \in G : p ∤ ∣ g ∣} .$

Brauer characters are defined on $G^{0}$ , not on all of $G$ .

Used by

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