• Finite Groups with Three Conjugacy Class Sizes of some Elements

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/122/03/0335-0337

• # Keywords

Conjugacy class sizes; 𝑝-nilpotent groups; finite groups.

• # Abstract

Let 𝐺 be a finite group. We prove as follows: Let 𝐺 be a 𝑝-solvable group for a fixed prime 𝑝. If the conjugacy class sizes of all elements of primary and biprimary orders of 𝐺 are $\{1,p^a,n\}$ with 𝑎 and 𝑛 two positive integers and $(p,n)=1$, then 𝐺 is 𝑝-nilpotent or 𝐺 has abelian Sylow 𝑝-subgroups.

• # Author Affiliations

1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, People’s Republic of China

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019

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