{
  "abstract": "We show that cohomological and homological goodness are equivalent. We prove that if $G$ is a coherent even Artin group or an even Artin group whose underlying graph does not contain 4-clique or a LERF Artin group then $G \\otimes G$ and $G \\wedge G$ are residually finite. Furthermore for $G$ a RAAG both $G \\otimes G$ and $G \\wedge G$ are residually $p$-finite for any prime integer $p$. For $G$ a limit group or a Coxeter group we show that $G \\wedge G$ is residually finite. For $G$ a soluble group of type $FP_{\\infty}$ we prove that the groups $\\X(G)$, $ν(G)$, $G \\wedge G$ are virtually residually $p$-finite for almost all primes $p$. For $G$ a generalised Baumslag-Solitar group of rank $n \\geq 1$ that is residually finite, we show that $G \\wedge G$ is residually finite. For $G = SL_n(\\Z)$ and $G = GL_n( \\mathbb{Z})$, $n \\geq 3$, we show that $G \\wedge G$ is residually finite.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02243",
  "author_total": 2,
  "authors": [
    {
      "name": "Lucas Barroso Rocha"
    },
    {
      "name": "Dessislava H. Kochloukova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bea0yend6gt9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02243",
  "fulltext_url": null,
  "id": "9bea0yend6gt9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02243",
  "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": "W7220437861",
  "pdf_url": "https://arxiv.org/pdf/2610.02243",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bea0yend6gt9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02243",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02243"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the residual finiteness of the non-abelian exterior square of some Artin groups, constructible soluble groups, generalised Baumslag-Solitar groups and $SL_n(\\Z)$",
  "title_text": "On the residual finiteness of the non-abelian exterior square of some Artin groups, constructible soluble groups, generalised Baumslag-Solitar groups and SL_n(Z)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/9bea0yend6gt9",
  "venue": "arXiv",
  "versions": []
}