Publication details
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
- General Mathematics
- Electronic version(s)
-
https://arxiv.org/abs/2105.01301 (Access:
Open)
https://doi.org/10.1007/s00605-021-01587-9 (Access: Open)
