{
  "abstract": "We show some sufficient conditions ( in terms of properties of $A$, $B$ and $X$) for the non-abelian exterior square $G \\wedge G$ to be residually finite, where $G $ is the wreath product $A \\wr B$ or the combinatorial wreath product $G = A \\wr_X B$, in the latter case $B$ is a free group. We prove that for the Grigorchuk group $G$ the non-abelian exterior square $G \\wedge G$ and the non-abelian tensor product $G \\otimes G$ are residually finite. We show conditions that imply that $A \\wr B$ is not (cohomologically) good in dimension $\\leq 2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10417",
  "author_total": 2,
  "authors": [
    {
      "name": "Ayrton Anjos Teixeira"
    },
    {
      "name": "Dessislava H. Kochloukova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mtb5h66v4xq9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10417",
  "fulltext_url": null,
  "id": "2mtb5h66v4xq9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10417",
  "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": "W7221042528",
  "pdf_url": "https://arxiv.org/pdf/2610.10417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mtb5h66v4xq9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group",
  "title_text": "On the residual finiteness of the non-abelian exterior square of wreath products and the Grigorchuk group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/2mtb5h66v4xq9",
  "venue": "arXiv",
  "versions": []
}