{
  "abstract": "Let $G$ be a finite solvable group and $V$ be a faithful completely reducible $G$-module. We improve previous bounds for the sizes of defect groups of blocks of solvable groups through an improved bound on vector stabilizers of $p$-nilpotent groups. Specifically, if $G$ is 2-nilpotent and $2 \\nmid |V|$, then there exists $v \\in V$ such that $\\mathbf{C}_G(v) \\leq \\mathbf{F}_4(G)$. Similarly, if $G$ is 3-nilpotent and $3 \\nmid |V|$, then there exists $v \\in V$ such that $\\mathbf{C}_G(v) \\leq \\mathbf{F}_5(G)$. Using these results, we conclude that $d(B) \\leq \\lfloor \\frac{9n}{10} \\rfloor$ when $O_p(G) = 1$ for $p = 2$ and $d(B) \\leq \\lfloor \\frac{19n}{21} \\rfloor$ when $O_p(G) = 1$ for $p = 3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30952",
  "author_total": 2,
  "authors": [
    {
      "name": "Chloe So"
    },
    {
      "name": "Yong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d97z9064e2edg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30952",
  "fulltext_url": null,
  "id": "d97z9064e2edg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30952",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223266498",
  "pdf_url": "https://arxiv.org/pdf/2610.30952",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d97z9064e2edg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30952",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30952"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orbits of $p$-Nilpotent Group Actions for Small Primes",
  "title_text": "Orbits of p-Nilpotent Group Actions for Small Primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/d97z9064e2edg",
  "venue": "arXiv",
  "versions": []
}