{
  "abstract": "Let $G$ be a finite solvable group such that, for any prime $p$ and any quotient $Q$ of $G$, there are two Sylow $p$-subgroups of $Q$ intersecting in $O_p(Q)$. Then, for every family $(P_i)_{i=1}^n$ of Sylow subgroups of $G$ for distinct primes $p_1,\\ldots,p_n$, there exists $x \\in G$ such that $P_i \\cap P_i^x = O_{p_i}(G)$ for all $i$. This covers groups of odd order, partially settling a conjecture of the second and fourth authors and unifying old results of Bialostocki and Mann on the intersection of nilpotent subgroups. We also prove a result for all symmetric and alternating groups, completing the proof of the conjecture for simple groups as initiated by Burness and the first author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28403",
  "author_total": 4,
  "authors": [
    {
      "name": "Hong Yi Huang"
    },
    {
      "name": "Francesca Lisi"
    },
    {
      "name": "Aluna Rizzoli"
    },
    {
      "name": "Luca Sabatini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1m525m2qkv4ze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28403",
  "fulltext_url": null,
  "id": "1m525m2qkv4ze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28403",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214181974",
  "pdf_url": "https://arxiv.org/pdf/2609.28403",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1m525m2qkv4ze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28403",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28403"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Sylow synchronization in finite groups: the good case",
  "title_text": "Sylow synchronization in finite groups: the good case",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1m525m2qkv4ze",
  "venue": "arXiv",
  "versions": []
}