{
  "abstract": "We study units in group rings of the Hantzsche-Wendt group. We construct a compatible system of non-trivial unitary units over $\\mathbb Z/2^n\\mathbb Z$ for every $n\\ge1$, and ``almost-group'' units over $\\mathbb Z/2\\mathbb Z$, meaning non-trivial units $u$ with the property that $u-g=u^{-1}-g^{-1}$ for some group element $g$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29273",
  "author_total": 3,
  "authors": [
    {
      "name": "Laurent Bartholdi"
    },
    {
      "name": "Iuliya Beloshapka"
    },
    {
      "name": "Roman Mikhailov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a4mr4d6c19xt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29273",
  "fulltext_url": null,
  "id": "a4mr4d6c19xt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29273",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7214395616",
  "pdf_url": "https://arxiv.org/pdf/2609.29273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a4mr4d6c19xt6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29273"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On symmetric and twisted-unitary modular units in group rings",
  "title_text": "On symmetric and twisted-unitary modular units in group rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/a4mr4d6c19xt6",
  "venue": "arXiv",
  "versions": []
}