On a bound of Cocke and Venkataraman

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Authors

  • Benjamin Sambale
  • Philipp Wellmann
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Details

Original languageEnglish
Pages (from-to)505–515
Number of pages11
JournalMonatshefte für Mathematik
Volume197
Issue number3
Early online date1 Jul 2021
Publication statusPublished - Mar 2022

Abstract

Let G be a finite group with exactly k elements of largest possible order m. Let q(m) be the product of gcd (m, 4) and the odd prime divisors of m. We show that | G| ≤ q(m) k 2/ φ(m) where φ denotes Euler’s totient function. This strengthens a recent result of Cocke and Venkataraman. As an application we classify all finite groups with k< 36. This is motivated by a conjecture of Thompson and unifies several partial results in the literature.

Keywords

    Finite groups, Maximal order, Number of elements

ASJC Scopus subject areas

Cite this

On a bound of Cocke and Venkataraman. / Sambale, Benjamin; Wellmann, Philipp.
In: Monatshefte für Mathematik, Vol. 197, No. 3, 03.2022, p. 505–515.

Research output: Contribution to journalArticleResearchpeer review

Sambale B, Wellmann P. On a bound of Cocke and Venkataraman. Monatshefte für Mathematik. 2022 Mar;197(3):505–515. Epub 2021 Jul 1. doi: 10.1007/s00605-021-01587-9
Sambale, Benjamin ; Wellmann, Philipp. / On a bound of Cocke and Venkataraman. In: Monatshefte für Mathematik. 2022 ; Vol. 197, No. 3. pp. 505–515.
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