{
  "abstract": "Every finite group (G, * ) determines a Petri net N G whose places are the elements of G and whose transitions realise the group's Cayley table: transition t a,b consumes one token from a and one from b and deposits one token in a * b. We develop this correspondence as a single connected story. Restricting N G to a subgroup H ≤ G gives a Subgroup Petri Net; separating a group element's carrier and control roles gives a control-copy net M G ; and restricting the control layer of M G to H makes one-step reachability on the carrier layer coincide exactly with the rightcoset partition of G by H, giving a Petri-net reading of Lagrange's theorem, |G| = [G : H] • |H|. We show every Group Petri Net carries a strictly decreasing token-sum functional, forcing boundedness and termination of every firing sequence, with the terminal marking independent of firing order for every initial marking exactly when G is abelian. All constructions are illustrated with fully worked, diagrammed examples: Z 3 for the basic construction, and S 3 , with the explicit subgroup H = {e, (1 2)} and its three coset blocks, for the subgroup, control-copy, and non-confluence phenomena.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Girish K P"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xxq6q0kdccpm.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "2xxq6q0kdccpm",
  "issns": [],
  "landing_url": "https://hal.science/hal-05846978v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05846978/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xxq6q0kdccpm.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:17Z",
      "native_id": "hal-05846978",
      "source": "hal",
      "url": "https://hal.science/hal-05846978v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Group Petri Nets: Structural and Algebraic Models for Finite Groups and Their Subgroups",
  "title_text": "Group Petri Nets: Structural and Algebraic Models for Finite Groups and Their Subgroups",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:17Z",
  "url": "https://research.draconitic.com/paper/2xxq6q0kdccpm",
  "venue": "HAL",
  "versions": []
}