{
  "abstract": "Let $G$ be the group of power series $x+a_2x^2+a_3x^3+\\cdots\\in R[[x]]$ under substitution, where $R$ is a commutative ring with $1\\neq 0$ of prime characteristic $p$. Given any $n\\geq 1$, the subgroup $K_n=\\{x+a_{n+1}x^{n+1}+a_{n+2}x^{n+2}+\\cdots\\,|\\, a_i\\in R\\}$ is normal in $G$, and the quotient $G_n=G/K_n$ is the group of truncated polynomials over $R$ of degree $\\leq n$ under substitution. In this paper, we compute the exponent of the image of $K_r$ in $G_n$, for all $r,n\\geq 1$, indicating in every case a family of elements realizing this exponent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11461",
  "author_total": 2,
  "authors": [
    {
      "name": "Agustín D'Alessandro"
    },
    {
      "name": "Fernando Szechtman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/849z2j4escec2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11461",
  "fulltext_url": null,
  "id": "849z2j4escec2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11461",
  "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",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7164424950",
  "pdf_url": "https://arxiv.org/pdf/2606.11461",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/849z2j4escec2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.11461",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11461"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Substitution groups of formal power series",
  "title_text": "Substitution groups of formal power series",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/849z2j4escec2",
  "venue": "arXiv",
  "versions": []
}