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CorollaryStatement: Literature-sourcedProof: AI-adaptedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-30
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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.

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A finite group with an irreducible complex character of degree greater than 1 is nonabelian

Statement

If a finite group G has an irreducible complex character χ with χ(1)>1, then G is nonabelian.

Facts & Assumptions

Given: A finite group G with an irreducible complex character χ such that χ(1)>1.

[F1]

A finite group is abelian if and only if all its irreducible complex characters have degree 1 (A finite group is abelian if and only if all its irreducible complex characters have degree 1).

Proof

technique · direct
1.1

If G were abelian, then [F1] would force every irreducible complex character of G to have degree 1.

F1givenassume-contra
2.1

That contradicts the hypothesis χ(1)>1. Therefore G is nonabelian.

step 1.1discharge-contradiction∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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