{
  "abstract": "According to the classical Skitovich--Darmois theorem, the Gaussian distribution on the real line is characterized by the independence of two linear forms of a finite number of independent random variables $ξ_j$. This theorem has been extended in various directions. In particular, S.G. Ghurye and I. Olkin established an analogous result for the case where $ξ_j$ are $n$-dimensional independent random vectors and the coefficients of the linear forms are invertible $n\\times n$ matrices. Subsequently, A.A. Zinger and later I.A. Ibragimov investigated linear forms of an infinite sequence of $n$-dimensional independent random vectors. In the present paper, we investigate, for the first time, linear forms of a sequence of independent random variables taking values in a second-countable locally compact Abelian group $X$ under either of the following conditions: $X$ contains no nontrivial compact subgroups, or $X$ contains no subgroups topologically isomorphic to the circle group and has a finite topological automorphism group. Furthermore, we investigate the case where the independent random variables take values in an $\\mathbf{a}$-adic solenoid $Σ_{\\mathbf{a}}$. In all these settings, the coefficients of the linear forms are topological automorphisms of the corresponding group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19346",
  "author_total": 1,
  "authors": [
    {
      "name": "Gennadiy Feldman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21xq11se2epz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19346",
  "fulltext_url": null,
  "id": "21xq11se2epz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19346",
  "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.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19346",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/21xq11se2epz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19346",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19346"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem",
  "title_text": "A Group Analogue of the Ghurye--Olkin--Ibragimov Theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/21xq11se2epz9",
  "venue": "arXiv",
  "versions": []
}