LemmaStatement: Literature-sourcedProof: Literature-sourcedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

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.

Characters of elementary groups are induced from linear characters

Statement

Every virtual character of a finite $p$ -elementary group is an integral linear combination of characters induced from linear characters of its subgroups.

Facts & Assumptions

[F1]

The cited prerequisite is Elementary groups are supersolvable.

Proof

Given: $E$ is $p$ -elementary and $ξ \in R (E)$ .

1.1

The elementary-group lemma makes $E$ supersolvable, and the monomiality theorem writes every irreducible constituent of $ξ$ as an induction of a linear character.

F1given

2.1

Add the resulting expressions with the integral multiplicities defining the virtual character $ξ$ . ∎

step 1.1

Depends on

Used by

Brauer induction Theorem

Dependency tree · two levels

19 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Wen-Wei Li, Yanqi Lake Lectures on Algebra I, Corollary 14.3.2 (standard reference, not scraped)