{
  "abstract": "In this paper, for a finite group $G$ and a positive integer $k$, we introduce the function $$ψ''_k(G)=\\dfrac{ψ_k(G)}{|G|^{k+1}}, \\quad \\text{where} \\quad ψ_k(G)=\\sum_{g \\in G}o(g)^k,$$ as the $k$-th generalization of the function $ψ''$, introduced by M. T{ă}rn{ă}uceanu. Different thresholds for cyclic, abelian, nilpotent and (super)solvable groups in terms of $k$ are obtained. It is shown that these thresholds often outperform similar thresholds derived from other parameters like $ψ'$ and $ψ''$. Moreover, considering $ψ''_k$ as a $(0,1]$-valued function, we study its injectivity, surjectivity and density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11804",
  "author_total": 3,
  "authors": [
    {
      "name": "Sayanta Chatterjee"
    },
    {
      "name": "Angsuman Das"
    },
    {
      "name": "Sauvik Poddar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8p4gxc6sacnbb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11804",
  "fulltext_url": null,
  "id": "8p4gxc6sacnbb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11804",
  "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": "W7221065365",
  "pdf_url": "https://arxiv.org/pdf/2610.11804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8p4gxc6sacnbb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.11804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A generalization of the sum of element orders function",
  "title_text": "A generalization of the sum of element orders function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/8p4gxc6sacnbb",
  "venue": "arXiv",
  "versions": []
}