{
  "abstract": "Given a group $G$, the prime graph of $G$, denoted $Γ(G)$, is the graph with vertex set the set of primes $p$ such that there exists an element of order $p$ in $G$, and such that there is an edge between primes $p$ and $q$ if and only if there exists an element of order $pq$ in $G$. Let $T$ be nonabelian finite simple group. A $T$-solvable group $G$ is a group such that there exists a finite subnormal series of $G$ such that each factor is either abelian or isomorphic to $T$. In this paper, we continue the classification of the prime graphs of $T$-solvable locally torsion groups and classify prime graphs of locally torsion metanilpotent groups using tools from model theory. We also classify the prime graphs of ultragroups with certain first-order properties and prove results on the number and type of certain classes of groups that can realize a given graph as a prime graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02696",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexa Renner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/aqee4w2t16t2p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02696",
  "fulltext_url": null,
  "id": "aqee4w2t16t2p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02696",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7220363813",
  "pdf_url": "https://arxiv.org/pdf/2610.02696",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/aqee4w2t16t2p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02696",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02696"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and $T$-Solvable Groups",
  "title_text": "Prime Graphs of Locally Torsion Ultragroups, Metanilpotent Groups, and T-Solvable Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/aqee4w2t16t2p",
  "venue": "arXiv",
  "versions": []
}