Kourovka Problem 21.150 - Rank Inequality for p-Group Extensions

Precise statement

For an extension $G = A \rtimes B$ of elementary abelian $p$-groups with $a \in A$ satisfying $C_B(a) = 1$, must $H = \langle a, B\rangle$ satisfy $\operatorname{rank}(Z(H) \cap H') \le \operatorname{rank}(B)$? An explicit extension violates the bound.

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.