Alphabeta Math
LemmaStatement: Literature-sourcedProof: Literature-sourcedPipeline-generatedverified 2026-09-26 (gpt-6-sol)
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.

[F2]

Every irreducible character of a finite supersolvable group is induced from a linear character of a subgroup (Finite supersolvable groups are monomial).

Proof

Given: E is p-elementary and ξ∈R(E).

1.1F1F2given

The elementary-group lemma makes E supersolvable, and [F2] writes every irreducible constituent of ξ as an induction of a linear character.

2.1step 1.1∎

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

Depends on

Used by

Dependency tree · two levels

20 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