{
  "abstract": "We study the geometry of a class of group extensions, containing permutational wreath products, which we call “permutational extensions”. We construct for all k∈ℕ a torsion group K k with growth function $$v_{K_k}(n)\\sim\\exp(n^{1-(1-\\alpha)^k}),\\qquad 2^{3-3/\\alpha}+2^{2-2/\\alpha}+2^{1-1/\\alpha}=2,$$ and a torsion-free group H k with growth function $$v_{H_k}(n)\\sim\\exp(\\log(n)n^{1-(1-\\alpha)^k}).$$ These are the first examples of groups of intermediate growth for which the asymptotics of their growth function is known. We construct a group of intermediate growth that contains the group of finitely supported permutations of a countable set as a subgroup. This gives the first example of a group of intermediate growth containing an infinite simple group as a subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "1011.5266",
  "author_total": 2,
  "authors": [
    {
      "name": "Laurent Bartholdi"
    },
    {
      "name": "Anna Erschler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ehqfc4w5t5b5z.bib",
  "cited_by": 41,
  "doi": "10.1007/s00222-011-0368-x",
  "fulltext_url": null,
  "id": "ehqfc4w5t5b5z",
  "issns": [
    "0020-9910",
    "1432-1297"
  ],
  "landing_url": "https://hal.science/hal-05849588v1",
  "language": "en",
  "licence": "CC-BY-NC",
  "licence_label": "CC BY-NC",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-nc/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-gr"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W2004779404",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s00222-011-0368-x.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": "Springer Verlag",
  "ris": "https://research.draconitic.com/paper/ehqfc4w5t5b5z.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:18Z",
      "native_id": "hal-05849588",
      "source": "hal",
      "url": "https://hal.science/hal-05849588v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-gr",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Growth of permutational extensions",
  "title_text": "Growth of permutational extensions",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/ehqfc4w5t5b5z",
  "venue": "Inventiones Mathematicae",
  "versions": []
}