{
  "abstract": "We solve a major open problem from [D. Dikranjan, D. Shakhmatov, Algebraic structure of pseudocompact groups, Memoirs AMS 633 (1998)] by describing abelian groups which admit a pseudocompact Hausdorff group topology. First, we prove that an abelian group G can be equipped with a pseudocompact Hausdorff group topology iff it can be decomposed into a direct sum G=B\\oplus H of a bounded torsion group B and agroup H satisfying |nH|=|H| for all positive integers $n$, such that both B and H admit a pseudocompact Hausdorff group topology. Second, for an unbounded abelian group G, we denote by m the minimal positive integer n such that |nG|=|kG| for all integers k\\ge n. Then G admits a pseudocompact group topology iff both G[m]={g\\in G: mg=0} and mG\\cong G/G[m] admit a pseudocompact Hausdorff group topology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03270",
  "author_total": 3,
  "authors": [
    {
      "name": "Dikran Dikranjan"
    },
    {
      "name": "Alejandro Dorantes-Aldama"
    },
    {
      "name": "Dmitri Shakhmatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqxsvmrhegeqt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03270",
  "fulltext_url": null,
  "id": "fqxsvmrhegeqt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03270",
  "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.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqxsvmrhegeqt.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03270"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A complete description of the algebraic structure of pseudocompact abelian groups",
  "title_text": "A complete description of the algebraic structure of pseudocompact abelian groups",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/fqxsvmrhegeqt",
  "venue": "arXiv",
  "versions": []
}