{
  "abstract": "For residually finite groups, we study the automorphism and normalizer groups of odometers and their symbolic extensions: Toeplitz subshifts. In relation to orbit equivalence theory, we show that two continuous orbit equivalent $G$-odometers have commensurable normalizers when $G=\\mathbb{Z}^d$, but that this result fails for other nilpotent groups $G$. The automorphism and normalizer groups of any Toeplitz subshift embed into those of its underlying odometer; despite this constraint, they exhibit considerable flexibility. For instance, we exhibit examples of low-complexity $G$-Toeplitz subshifts whose centralizer is isomorphic to $G$ (or, at the other extreme, restricted to its center) yet whose normalizer group is as large as possible.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06488",
  "author_total": 2,
  "authors": [
    {
      "name": "Jaime Gómez"
    },
    {
      "name": "Samuel Petite"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83whps54tsk77.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06488",
  "fulltext_url": null,
  "id": "83whps54tsk77",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06488",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7220684196",
  "pdf_url": "https://arxiv.org/pdf/2610.06488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83whps54tsk77.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.06488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "On the centralizer and normalizer groups of odometers and Toeplitz subshifts",
  "title_text": "On the centralizer and normalizer groups of odometers and Toeplitz subshifts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/83whps54tsk77",
  "venue": "arXiv",
  "versions": []
}