{
  "abstract": "We study prime graph complements of $\\mathcal{A}_n$-solvable groups, focusing on the cases $\\mathcal{A}_{11}$ and $\\mathcal{A}_{13}$. These provide the first classifications of $T$-solvable groups for which $|π(T)|>4$. We develop structural and representation-theoretic tools for analyzing the possible prime graph complements and use them to obtain complete characterizations for both $\\mathcal{A}_{11}$-solvable and $\\mathcal{A}_{13}$-solvable groups. The methods introduced also provide a framework for studying analogous classification problems for larger alternating groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24325",
  "author_total": 6,
  "authors": [
    {
      "name": "Logan Abounader"
    },
    {
      "name": "Austin Bell"
    },
    {
      "name": "April Beun"
    },
    {
      "name": "Elvis Cabrera"
    },
    {
      "name": "Dakota Nobuyuki Goto"
    },
    {
      "name": "Thomas Michael Keller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/esv2byn3cvk54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24325",
  "fulltext_url": null,
  "id": "esv2byn3cvk54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24325",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7222993858",
  "pdf_url": "https://arxiv.org/pdf/2610.24325",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/esv2byn3cvk54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24325",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24325"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The prime graph complements of $\\mathcal{A}_{11}$- and $\\mathcal{A}_{13}$-solvable groups",
  "title_text": "The prime graph complements of 𝒜_11- and 𝒜_13-solvable groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/esv2byn3cvk54",
  "venue": "arXiv",
  "versions": []
}