{
  "abstract": "For a finite group G , the prime graph Γ ( G ) (also known as Gruenberg-Kegel graph) is defined to be the graph where the vertices are the primes that divide | G | such that two vertices p and q share an edge if and only if there is an element of order pq in G . The prime graphs of solvable groups have been classified. The prime graphs of groups whose noncyclic composition factors are isomorphic to a single nonabelian simple group T where | T | is divisible by three or four distinct primes have been classified except for the cases where T = PSL ( 2 , q ) for q ≠ 2 5 and | PSL ( 2 , q ) | is divisible by exactly four primes. In this paper, we provide criteria for general classification results for certain classes of T , and then use them to classify the prime graphs of some T -solvable groups for T a suitably small PSL ( 2 , q ) -group. We also provide general results on the prime graphs of T -solvable groups where T is a member of the possibly infinite family of groups PSL ( 2 , 2 f ) such that f ≥ 5 , f is prime, and | PSL ( 2 , 2 f ) | is divisible by exactly four primes. This is the first paper to prove general results about the prime graphs of T -solvable groups where T belongs to a large (probably infinite) family of groups.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA",
    "Department of Mathematics, Willamette University, 900 State St., Salem, OR 97301, USA",
    "Department of Mathematics, Rose-Hulman Institute of Technology, 5500 Wabash Ave., Terre Haute, IN 47803, USA; Corresponding author.",
    "Department of Mathematics, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA",
    "Department of Mathematics, University of Pennsylvania, 209 S 33rd St, Philadelphia, PA 19104, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Thomas Michael Keller"
    },
    {
      "affs": [
        1
      ],
      "name": "Zachary Martin"
    },
    {
      "affs": [
        2
      ],
      "name": "Alexa Renner"
    },
    {
      "affs": [
        3
      ],
      "name": "Gabriel Roca"
    },
    {
      "affs": [
        4
      ],
      "name": "Eric Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c8m8kvnapsez1.bib",
  "cited_by": 0,
  "doi": "10.1016/j.jaca.2026.100051",
  "fulltext_url": "http://www.sciencedirect.com/science/article/pii/S2772827726000094",
  "id": "c8m8kvnapsez1",
  "issns": [
    "2772-8277"
  ],
  "landing_url": "https://doi.org/10.1016/j.jaca.2026.100051",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
  ],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/c8m8kvnapsez1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:54Z",
      "native_id": "58ee644113954a668c60c7f852484d67",
      "source": "doaj",
      "url": "https://doi.org/10.1016/j.jaca.2026.100051"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Criteria for classifying prime graphs of PSL(2,",
  "title_text": "Criteria for classifying prime graphs of PSL(2,",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:54Z",
  "url": "https://research.draconitic.com/paper/c8m8kvnapsez1",
  "venue": "Journal of Computational Algebra",
  "versions": []
}