{
  "abstract": "We obtain a characterization of finite non-$p$-groups with five automorphism orbits. In the solvable case of Fitting height $3$, the groups are precisely $S_4$ and $C_2^4\\rtimes D_{10}$. Moreover, the corresponding fixed-point subspaces form a spread in a finite projective space. For Fitting height $2$, we distinguish the possible structures according to the number of prime divisors of $|G|$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00786",
  "author_total": 1,
  "authors": [
    {
      "name": "Julia Kato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9kf1s37y9trq8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00786",
  "fulltext_url": null,
  "id": "9kf1s37y9trq8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00786",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7215679692",
  "pdf_url": "https://arxiv.org/pdf/2610.00786",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9kf1s37y9trq8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00786",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00786"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Non-$p$-Groups with 5 Automorphism Orbits",
  "title_text": "Finite Non-p-Groups with 5 Automorphism Orbits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/9kf1s37y9trq8",
  "venue": "arXiv",
  "versions": []
}