{
  "abstract": "We prove that if $G$ is a residually finite group, $\\widehat{G}$ is its profinite completion and the map $H_2(G, \\mathbb{Z}) $ $ \\to H_2(\\widehat{G}, \\widehat{\\mathbb{Z}}),$ induced by the canonical map $G \\to \\widehat{G}$, is injective, then the non-abelian exterior square $G \\wedge G$ is residually finite. We show that if $G$ is a finitely presented centre-by-metabelian group then $ν(G)$, the non-abelian tensor product $G \\otimes G$ and the non-abelian tensor square $G \\wedge G$ are residually finite. Furthermore we prove that if $G$ be a finitely presented metabelian group then the weak commutative construction $\\X(G)$ is residually finite. We discuss a criterion for the $q$-exterior square $G \\wedge^q G$ to be residually finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34057",
  "author_total": 3,
  "authors": [
    {
      "name": "Ayrton Anjos Teixeira"
    },
    {
      "name": "Lucas Barroso Rocha"
    },
    {
      "name": "Dessislava H. Kochloukova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2rgjcyqjp1h6h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34057",
  "fulltext_url": null,
  "id": "2rgjcyqjp1h6h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34057",
  "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": "W7214748744",
  "pdf_url": "https://arxiv.org/pdf/2609.34057",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2rgjcyqjp1h6h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34057",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34057"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the residual finiteness of the non-abelian tensor square $G \\otimes G$, the non-abelian exterior square $G \\wedge G$ and the weak commutativity construction $\\X(G)$",
  "title_text": "On the residual finiteness of the non-abelian tensor square G ⊗ G, the non-abelian exterior square G ∧ G and the weak commutativity construction X(G)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2rgjcyqjp1h6h",
  "venue": "arXiv",
  "versions": []
}