{
  "abstract": "We study the probability that certain laws are satisfied on infinite groups, focusing on elements sampled by random walks. For several group laws, including the metabelian one, we construct examples of infinite groups for which the law holds with high probability, but the group does not satisfy the law virtually. On the other hand, we show that if an infinite group satisfies the law x 2 = 1 with positive probability, then it is virtually abelian.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Bar-Ilan University, Ramat Gan, 52900, Israel",
    "Institut für Informatik, Westälische Wilhelms-Universität Münster, 48149, Münster, Germany",
    "Department of Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Gideon Amir",
      "orcid": "0000-0001-7738-0441"
    },
    {
      "affs": [
        0
      ],
      "name": "Guy Blachar",
      "orcid": "0009-0001-6829-5461"
    },
    {
      "affs": [
        1
      ],
      "name": "Maria Gerasimova",
      "orcid": "0000-0001-6311-2630"
    },
    {
      "affs": [
        2
      ],
      "name": "Gady Kozma",
      "orcid": "0000-0003-3033-9235"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3a2ddjsqngwft.bib",
  "cited_by": 5,
  "doi": "10.1007/s11856-026-2943-2",
  "fulltext_url": null,
  "id": "3a2ddjsqngwft",
  "issns": [
    "0021-2172",
    "1565-8511"
  ],
  "landing_url": "https://doi.org/10.1007/s11856-026-2943-2",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W4366460488",
  "pdf_url": "https://link.springer.com/content/pdf/10.1007/s11856-026-2943-2.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": "Hebrew University of Jerusalem",
  "ris": "https://research.draconitic.com/paper/3a2ddjsqngwft.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T13:21:00Z",
      "native_id": "W4366460488",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s11856-026-2943-2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Finite Group Theory Research",
      "subfield": "combinatorics"
    }
  ],
  "title": "Probabilistic laws on infinite groups",
  "title_text": "Probabilistic laws on infinite groups",
  "type": "peer-reviewed",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/3a2ddjsqngwft",
  "venue": "Israel Journal of Mathematics",
  "versions": []
}