{
  "abstract": "We investigate conditions under which a semidirect product $G=HN$, and in particular a restricted wreath product, is an equational domain. For a variety of groups $\\X$, we study semidirect products of $\\XT$-groups (groups where $\\langle A, B\\rangle \\in\\X$ for any two $\\X$-subgroups $A$ and $B$ with nontrivial intersection) and $\\CSX$-groups (groups where all maximal $\\X$-subgroups are malnormal). We pay particular attention to split Frobenius groups and investigate conditions under which such groups are $\\XT$- or $\\CSX$-groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32643",
  "author_total": 2,
  "authors": [
    {
      "name": "Omar Al-Raisi"
    },
    {
      "name": "Mohammad Shahryari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/120svsvqj44mm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32643",
  "fulltext_url": null,
  "id": "120svsvqj44mm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32643",
  "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": "W7223667242",
  "pdf_url": "https://arxiv.org/pdf/2610.32643",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/120svsvqj44mm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32643",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32643"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Split Frobenius Groups, Equational Domains, $\\mathfrak{X}T$- and $CS\\mathfrak{X}$-groups",
  "title_text": "Split Frobenius Groups, Equational Domains, XT- and CSX-groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/120svsvqj44mm",
  "venue": "arXiv",
  "versions": []
}