{
  "abstract": "In this paper, we describe the centroid (according to S. Lioutikov and A. Myasnikov) of an arbitrary finitely generated graph two-step nilpotent Hall exponential group over a binomial domain whose commutativity graph has no central vertices. Based on this description, we prove that if the non-commutativity graph of such a group has exactly one connected component and the group is non-Abelian, then the group is rigid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40680",
  "author_total": 1,
  "authors": [
    {
      "name": "Ivan M. Buchinskiy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/853j9b0cvs5ef.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40680",
  "fulltext_url": null,
  "id": "853j9b0cvs5ef",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40680",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/853j9b0cvs5ef.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Centroids Of Partially Commutative Two-step Nilpotent Groups",
  "title_text": "Centroids Of Partially Commutative Two-step Nilpotent Groups",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/853j9b0cvs5ef",
  "venue": "arXiv",
  "versions": []
}