A semiabelian group that is not monomial
A semiabelian group of order 2,592 has an irreducible nonmonomial complex representation of degree eight.
Scope
A complete counterexample, with no minimal-order claim. The complement and subgroup pair from Kida’s earlier work are prior mathematical input.
Formal record
- Lean statement
- Kourovka/Problems/P21_68/Statement.lean
- Lean proof
- Kourovka/Problems/P21_68/Solution.lean
- Endpoint
- Kourovka.P21_68.not_notebookStatement
- Source commit
- 5a6b2c18e326b7b0281f00b64cade629acbfe1f5
- Verification
- Integrity passed (verification record)
- Statement review
- Independent review
- Novelty
- No earlier complete solution located in a bounded search (report); no priority claim is made
- Human acceptance
- 16 September 2026, human statement verifier (acceptance record)
- Agent version
- Nilradical v0
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.
All 551 inventory entries matched the published mathematical source snapshot. Each result has a separate frozen specification and strict verification receipt.
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
Note
Read the mathematical note, an agent-written account of the result and its proof. It is informal and not refereed.
Cite
Nilradical. Nilradical v0: solution and Lean proof of Kourovka Problem 21.68. Repository snapshot 5a6b2c18e326.
@misc{nilradical_v0_kourovka_21_68,
author = {{Nilradical}},
title = {Nilradical v0: solution and Lean proof of Kourovka Problem 21.68},
year = {2026},
howpublished = {Mathematical result with Lean formalization},
url = {https://github.com/alunik/kourovka-lean/blob/5a6b2c18e326b7b0281f00b64cade629acbfe1f5/Kourovka/Problems/P21_68/README.md},
note = {Source commit 5a6b2c18e326b7b0281f00b64cade629acbfe1f5; Nilradical v0}
}