{
  "abstract": "Let $\\X$ be a variety of groups. A group $G$ is $\\CSX$ if its maximal $\\X$-subgroups are malnormal. We prove that the amalgamated free product of two $\\CSX$-groups with a malnormal amalgam and without any involutions is again $\\CSX$. Using this, we describe conditions under which the HNN-extension of a $\\CSX$-group is $\\CSX$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17954",
  "author_total": 2,
  "authors": [
    {
      "name": "Omar Al-Raisi"
    },
    {
      "name": "Mohammad Shahryari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vnnz0hd1dgtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17954",
  "fulltext_url": null,
  "id": "6vnnz0hd1dgtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17954",
  "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",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7221760511",
  "pdf_url": "https://arxiv.org/pdf/2610.17954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vnnz0hd1dgtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$\\mathrm{CS}\\mathfrak{X}$-groups and free constructions",
  "title_text": "CSX-groups and free constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/6vnnz0hd1dgtr",
  "venue": "arXiv",
  "versions": []
}