{
  "abstract": "Let $G$ be a finite group. L. Morgana, C. E. Praeger, A.E. Zalesski \\cite {MOR} introduced the notion of almost maximal subgroup of $G$. A subgroup $H$ of $G$ is said to be almost maximal in $G$ if $N_G(H)$ is maximal in $G$. In this paper, let $AM(G)$ denote the number of conjugacy classes of all almost maximal subgroups of $G$. First, we prove that $G$ is Dedekindian if and only if $AM(G)=0$. Second, we show that the finite groups with $AM(G)\\leq 1$ are supersolvable. Furthermore, we characterize the structure of finite groups with $AM(G)=1$. Final, we investigate a lower bound of $AM(G)$ for certain non-solvable groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02532",
  "author_total": 3,
  "authors": [
    {
      "name": "Wei Meng"
    },
    {
      "name": "Boru Zhang"
    },
    {
      "name": "Jiakuan Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3g3t1w2ac5czn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02532",
  "fulltext_url": null,
  "id": "3g3t1w2ac5czn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02532",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02532",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3g3t1w2ac5czn.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02532",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02532"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Groups with Few Almost Maximal Subgroups",
  "title_text": "Finite Groups with Few Almost Maximal Subgroups",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/3g3t1w2ac5czn",
  "venue": "arXiv",
  "versions": []
}