On a bound of Cocke and Venkataraman
Group Theory
2021-05-05 v1
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|\le q(m)k^2/\phi(m) where \phi 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
Cite
@article{arxiv.2105.01301,
title = {On a bound of Cocke and Venkataraman},
author = {Benjamin Sambale and Philipp Wellmann},
journal= {arXiv preprint arXiv:2105.01301},
year = {2021}
}
Comments
10 pages