Nilradical

A semiabelian group with a nonmonomial character

Kourovka Notebook · 21.68Answer: NegativeNilradical v0

Cited by Meta AI in Semiabelian Groups Need Not Be Monomial ().

The result

Counterexample

A semiabelian group of order 2592 has an irreducible complex character of degree 8 that is not induced from a linear character of any subgroup.

Scope of the contribution

A complete counterexample, with no minimal-order claim. The complement and subgroup pair from Kida’s earlier work are prior mathematical input.

Construction, proof and formalization

Mathematical dependencies and credit

Counterexample, proof and formalization by Nilradical v0. The construction uses Kida’s semiabelian complement.

  • Nilradical v0 — discovery, proof and formalization
  • M. Kida — conjecture and prior mathematical input
  • Tau Ceti contributors — adapted induction infrastructure

Proof source

The source and theorem endpoints refer to the pinned revision.

  • Kourovka.P21_68.not_notebookStatement

Source revision
5a6b2c18e326b7b0281f00b64cade629acbfe1f5

Proof sourceProof overview

Recorded checks and review

Recorded proof checks

Strict verification passed on 16 September 2026 for 7 endpoints: fresh compilation, frozen-statement comparison, a three-axiom policy, and checks by both Lean and Nanoda. Independent statement review passed. Final human statement acceptance was recorded on 2026-09-16 for the linked proof snapshot.

Recorded proof checks record

Statement review

Recorded comparison of the formal statement and its intended mathematical scope.

Statement review record

Human statement acceptance

Human statement acceptance for this pinned source snapshot. This is separate from refereeing of the exposition or a priority determination.

Human statement acceptance record

Historical literature review

A dated, bounded literature search. This historical review is not a certificate of absolute priority; current related work is listed separately.

Historical literature review record

Mathematical note

Agent-generated exposition; not refereed, revised . The note does not change the proof statement or its recorded checks.

Read the mathematical note

Cite this contribution

Nilradical v0. A semiabelian group with a nonmonomial character. Cite the original mathematics and the formalization you use, retaining the source credits above.

BibTeX citation
@misc{nilradical_kourovka_21_68,
  author = {{Nilradical}},
  title = {A semiabelian group with a nonmonomial character},
  url = {https://github.com/alunik/kourovka-lean/blob/5a6b2c18e326b7b0281f00b64cade629acbfe1f5/Kourovka/Problems/P21_68/README.md},
  note = {Source revision 5a6b2c18e326b7b0281f00b64cade629acbfe1f5}
}

Using this contribution does not require adding Nilradical or anyone from the project as a coauthor.