{
  "abstract": "We develop a projection and fibering method for sets of small combinatorial doubling in (not necessarily abelian) discrete groups. As an application, in the abelian case we prove that, if $A$ is finite, the ambient group has exponent $r$, and $|A+A|\\leq K|A|$, then \\[ |\\langle A\\rangle|\\leq r^{(2+o(1))K}|A|. \\] This answers a question of Ruzsa with an optimal leading coefficient, independent of Fox--Pham. The main ingredient is a discrete version of a fiber spillover argument. For sets in $2$-step nilpotent groups of exponent $r$, we also prove that $|A^3|\\leq K|A|$ implies $|\\langle A\\rangle|\\leq r^{(2+o_K(1))K}|A|$. The proof combines the abelian theorem with a weighted averaging of central fibers and commutators.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13021",
  "author_total": 3,
  "authors": [
    {
      "name": "Yifan Jing"
    },
    {
      "name": "Zuxiang Kong"
    },
    {
      "name": "Souktik Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w5pb2zj55nq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13021",
  "fulltext_url": null,
  "id": "3w5pb2zj55nq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13021",
  "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.GR"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7212737495",
  "pdf_url": "https://arxiv.org/pdf/2609.13021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w5pb2zj55nq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13021"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Projection and fibering in groups of bounded exponent",
  "title_text": "Projection and fibering in groups of bounded exponent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/3w5pb2zj55nq0",
  "venue": "arXiv",
  "versions": []
}