Finite groups whose conjugacy class sizes of primary and biprimary elements are Hall numbers

Changguo Shao                <meta name=

2020/96/3-4 (2) — DOI: 10.5486/PMD.2020.8464 — pp. 281-289

Finite groups whose conjugacy class sizes of primary and biprimary elements are Hall numbers

Authors: Changguo Shao and Qinhui Jiang

Abstract:

Let $G$ be a finite group, and $m$ be a positive integer. Then $m$ is called a Hall number of $G$ if $m$ is a positive divisor of $|G|$ satisfying ${\rm gcd}(|G|/m,m)=1$. In this paper, we classify finite groups whose conjugacy class sizes of primary and biprimary elements are Hall numbers.

Keywords: finite groups, conjugacy class sizes, primary and biprimary elements, Hall numbers

Mathematics Subject Classification: 20E45, 20D10