{
  "abstract": "Given a prime $p$, the Nottingham group $G(p)$ is the group of formal power series $x+a_2x^2+a_3x^3+\\cdots$, $a_i\\in{\\bf Z}/p{\\bf Z}$, under substitution. For $n\\geq 1$, we write $G_n(p)$ for the quotient of $G(p)$ by its normal subgroup $K_n=\\{x+a_{n+1}x^{n+1}+a_{n+2}x^{n+2}+\\cdots\\,|\\, a_i\\in {\\bf Z}/p{\\bf Z}\\}$, namely the group of truncated polynomials $x+a_2x^2+\\cdots+a_nx^n$, $a_i\\in {\\bf Z}/p{\\bf Z}$, under substitution, which is a $p$-group of order $p^{n-1}$ generated by $x+x^2,\\dots,x+x^n$. In this paper, we determine the power-commutator presentation of $G_{15}(p)$ relative to $x+x^2,\\dots,x+x^{15}$. This, in turn, automatically gives the power-commutator presentation of $G_{n}(p)$ relative to $x+x^2,\\dots,x+x^{n}$ for any $1\\leq n<15$, as well as the initial segments of the power and commutator relations in $G_{n}(p)$ corresponding to $x+x^2,\\dots,x+x^{15}$ for any $n>15$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01469",
  "author_total": 1,
  "authors": [
    {
      "name": "Fernando Szechtman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feykz70gsv01n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01469",
  "fulltext_url": null,
  "id": "feykz70gsv01n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01469",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7216224234",
  "pdf_url": "https://arxiv.org/pdf/2610.01469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feykz70gsv01n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A power-commutator presentation for the group of truncated polynomials under substitution",
  "title_text": "A power-commutator presentation for the group of truncated polynomials under substitution",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/feykz70gsv01n",
  "venue": "arXiv",
  "versions": []
}