{
  "abstract": "We will answer a problem of Dotsenko that asks for a tight upper bound on the rank of subgroups given a maximum length for its generators. Then, we will use the same tools to answer a longstanding problem of Grigorchuk in the 10th edition of the Kourovka notebook. We accomplish this using Stallings foldings and simple graph theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00382",
  "author_total": 2,
  "authors": [
    {
      "name": "Lucy Koch-Hyde"
    },
    {
      "name": "Éamonn Olive"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wwd0pdmrsjnp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00382",
  "fulltext_url": null,
  "id": "8wwd0pdmrsjnp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00382",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7206189671",
  "pdf_url": "https://arxiv.org/pdf/2609.00382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wwd0pdmrsjnp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.00382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00382"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Two problems about bases and independent sets in free groups",
  "title_text": "Two problems about bases and independent sets in free groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/8wwd0pdmrsjnp",
  "venue": "arXiv",
  "versions": []
}