{
  "abstract": "The prime graph of a finite group $G$ is the graph $Γ(G)$ with vertex set the set of prime divisors $π(G)$ of $|G|$ and an edge between vertices $p, q\\inπ(G)$ if and only if there exists an element $g\\in G$ with order $o(g) = pq$. Given a finite nonabelian simple group $T$, a group $G$ is $T$-solvable if there exists a composition series of $G$ such that every composition factor is either abelian or isomorphic to $T$. In this paper, we introduce the prime graph of an infinite group, the graph $Γ(G)$ with vertex set $π(G) = \\{o(g):g\\in G\\text{ and }o(g)\\text{ is prime}\\}$ and an edge between $p,q\\inπ(G)$ if and only if there exists an element $g\\in G$ with order $pq$, and generalize several results on the prime graphs of finite solvable and $T$-solvable groups to results on the prime graphs of members of certain classes of infinite solvable and $T$-solvable groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02102",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexa Renner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vs9ff9j3b13r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02102",
  "fulltext_url": null,
  "id": "6vs9ff9j3b13r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02102",
  "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": "W7216438046",
  "pdf_url": "https://arxiv.org/pdf/2610.02102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vs9ff9j3b13r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Prime Graphs of Infinite Groups",
  "title_text": "Prime Graphs of Infinite Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/6vs9ff9j3b13r",
  "venue": "arXiv",
  "versions": []
}