2403.16364
On maximal subgroups of ample groups
Rostislav Grigorchuk, Yaroslav Vorobets
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 7.6 proves that a maximal subgroup H not acting minimally must be a set-stabilizer StG(Y), and that any maximal stabilizer acts minimally on Y, using Lemmas 7.2 and 7.5. The candidate’s proof reaches the same conclusions via a different route: it selects an H-minimal closed subset Y by a compactness/Zorn argument and then uses maximality to show H = StG(Y), so the induced action is minimal by construction. Thus both are correct; the proofs differ in method and strength (the paper handles any Y with maximal stabilizer, while the model proves minimality for its particular Zorn-chosen Y).
Referee report (LaTeX)
\textbf{Recommendation:} no revision
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The theorem under audit is correctly proven in the paper and is central to the broader classification of maximal subgroups. The model’s alternative argument is valid and offers a compact route via an H-minimal closed set; it complements the paper without exposing flaws. The exposition is clear and the logical dependencies are appropriate.