{
  "abstract": "We determine exactly which proper multiplicative subgroups of a prime field can be represented as a restricted sumset of the form $A\\mathbin{\\widehat{+}} A=\\{a+a':a,a'\\in A,\\ a\\ne a'\\}$. We prove that a proper multiplicative subgroup $H\\le\\mathbb F_p^*$ cannot satisfy $H=A\\mathbin{\\widehat{+}} A$ whenever $|H|\\ge7$, and that this threshold is sharp. In fact, such a decomposition exists precisely when $|H|\\in\\{1,3,6\\}$, and we classify all decompositions in these exceptional cases. This gives a sharp, complete resolution of the restricted-sumset analogue of the generalized Sárközy conjecture over prime fields. This significantly extends and refines previous results of Shkredov and Yip.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.25711",
  "author_total": 2,
  "authors": [
    {
      "name": "Chi Hoi Yip"
    },
    {
      "name": "Semin Yoo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abtnp1scx3eyk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.25711",
  "fulltext_url": null,
  "id": "abtnp1scx3eyk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.25711",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7171615585",
  "pdf_url": "https://arxiv.org/pdf/2607.25711",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abtnp1scx3eyk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2607.25711",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.25711"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Multiplicative subgroups are not restricted sumsets",
  "title_text": "Multiplicative subgroups are not restricted sumsets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/abtnp1scx3eyk",
  "venue": "arXiv",
  "versions": []
}