On a bound of Cocke and Venkataraman

authored by

Benjamin Sambale, Philipp Wellmann

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Article

Journal

Monatshefte für Mathematik

Volume

197

Pages

505–515

No. of pages

11

ISSN

0026-9255

Publication date

03.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://arxiv.org/abs/2105.01301 (Access: Open)
https://doi.org/10.1007/s00605-021-01587-9 (Access: Open)