## Taiwanese Journal of Mathematics

### The Influence of Conjugacy Class Sizes on the Structure of Finite Groups

#### Abstract

Let $G$ be a group. The question of how certain arithmetical conditions on the sizes of the conjugacy classes of $G$ influence the group structure has been studied by many authors. In this paper, we investigate the influence of conjugacy class sizes of primary and biprimary elements on the structure of $G$. A criterion for a group to have abelian Sylow subgroups is given and some well-known results on Baer-groups are generalized.

#### Article information

Source
Taiwanese J. Math., Volume 21, Number 4 (2017), 719-725.

Dates
Revised: 2 November 2016
Accepted: 25 November 2016
First available in Project Euclid: 27 July 2017

https://projecteuclid.org/euclid.twjm/1501120829

Digital Object Identifier
doi:10.11650/tjm/7083

Mathematical Reviews number (MathSciNet)
MR3684382

Zentralblatt MATH identifier
06871341

#### Citation

Chen, Ruifang; Zhao, Xianhe. The Influence of Conjugacy Class Sizes on the Structure of Finite Groups. Taiwanese J. Math. 21 (2017), no. 4, 719--725. doi:10.11650/tjm/7083. https://projecteuclid.org/euclid.twjm/1501120829

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