{
  "abstract": "We introduce a kernel--wreath construction for finite skew braces. Let $C$ be a finite skew brace, write $(C,+)=A$ and $(C,\\circ)=R$, and let $χ:R\\twoheadrightarrow T$ be an epimorphism onto a non-trivial finite abelian group. We show that a natural index-$|T|$ kernel in the permutational wreath product $R\\wr T$ acts regularly on $A^T$, and hence defines a new skew brace $\\KT_T(C,χ)$ with additive group $A^{|T|}$. The construction preserves every finite abelian quotient of the multiplicative group, as well as solvability, and contains the seed brace $C$ as a diagonal subbrace. It can therefore be iterated indefinitely. More precisely, if $Q$ is a non-trivial finite abelian quotient of $R$ and $p\\inπ(Q)$, then one obtains an infinite tower \\[ C=C_0\\hookrightarrow C_1\\hookrightarrow C_2\\hookrightarrow\\cdots \\] with $(C_m,+)\\cong A^{p^m}$ for every $m\\geq0$. Our main permanence result shows that if $C$ is simple and is not a trivial skew brace, then $\\KT_T(C,χ)$ is again simple. Consequently, a single simple seed whose multiplicative group has a non-trivial finite abelian quotient gives rise to infinite families of finite simple skew braces. In particular, starting from suitable solvable regular subgroups of the holomorph of a finite non-abelian simple group $S$, we obtain infinite families of simple skew braces with additive groups $S^{p^m}$ and solvable multiplicative groups. Further applications are given to the simple skew braces of order $12$ and to Byott's family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20401",
  "author_total": 1,
  "authors": [
    {
      "name": "Marco Damele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh2pe3fjy8mp3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20401",
  "fulltext_url": null,
  "id": "bh2pe3fjy8mp3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20401",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7213578095",
  "pdf_url": "https://arxiv.org/pdf/2609.20401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh2pe3fjy8mp3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Kernel--wreath constructions and infinite families of finite simple skew braces",
  "title_text": "Kernel--wreath constructions and infinite families of finite simple skew braces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/bh2pe3fjy8mp3",
  "venue": "arXiv",
  "versions": []
}