{
  "abstract": "A classical theorem of Gaschütz states that an abelian normal subgroup N of a finite group G has a complement in G whenever it has a complement in some subgroup H with $N \\leq H \\leq G$ and gcd(|N|, [G:H]) = 1. We characterize the finite groups N for which this theorem remains valid without the abelian hypothesis: this is the case if and only if $Z(N) \\cap N' = 1$ and N has a complement in a quotient of the holomorph Hol(N) by a diagonal copy of N'. This completes a previous paper by the second author.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27579",
  "author_total": 2,
  "authors": [
    {
      "name": "Stefanos Aivazidis"
    },
    {
      "name": "Benjamin Sambale"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30x3ymbzv5q9g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27579",
  "fulltext_url": null,
  "id": "30x3ymbzv5q9g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27579",
  "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": "W7204843355",
  "pdf_url": "https://arxiv.org/pdf/2608.27579",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30x3ymbzv5q9g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27579"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Groups satisfying Gaschütz's complement theorem",
  "title_text": "Groups satisfying Gaschütz's complement theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/30x3ymbzv5q9g",
  "venue": "arXiv",
  "versions": []
}