Details
| Original language | English |
|---|---|
| Pages (from-to) | 505–515 |
| Number of pages | 11 |
| Journal | Monatshefte für Mathematik |
| Volume | 197 |
| Issue number | 3 |
| Early online date | 1 Jul 2021 |
| Publication status | Published - 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
- Mathematics(all)
- General Mathematics
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In: Monatshefte für Mathematik, Vol. 197, No. 3, 03.2022, p. 505–515.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On a bound of Cocke and Venkataraman
AU - Sambale, Benjamin
AU - Wellmann, Philipp
N1 - Funding Information: The first author is supported by the German Research Foundation (SA 2864/1-2 and SA 2864/3-1).
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
KW - Finite groups
KW - Maximal order
KW - Number of elements
UR - http://www.scopus.com/inward/record.url?scp=85125609534&partnerID=8YFLogxK
U2 - 10.1007/s00605-021-01587-9
DO - 10.1007/s00605-021-01587-9
M3 - Article
VL - 197
SP - 505
EP - 515
JO - Monatshefte für Mathematik
JF - Monatshefte für Mathematik
SN - 0026-9255
IS - 3
ER -