Kourovka Problem 3.46 - Maximal Locally Soluble Normal Subgroups

Precise statement

Does there exist a group with more than one but only finitely many maximal locally soluble normal subgroups? An explicit group with exactly two settles it.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

Aristotle

The solution was discovered autonomously by Aristotle and formalized in Lean; the human authors curated the exposition.

Provider: Harmonic · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Autonomously discovered and formally verified in Lean by Aristotle; author-curated arXiv preprint covering eight Kourovka Notebook problems.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-20

   arXiv:2607.17477 - On some problems from the Kourovka Notebook

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.