On Class Size of p-Singular Elements in Finite Groups

Abstract

The object of this article is to study the connection between the structure of a finite group and the conjugacy class sizes of the p-singular elements of a finite group. The finite groups G in which every conjugacy class size of the p-singular elements satisfies some given arithmetic conditions are classified.

Key Words:

• Class size
• Finite group
• p-Singular element

2000 Mathematics Subject Classification:

• 20E45

ACKNOWLEDGMENT

The authors are grateful to the anonymous referees for their helpful comments and suggestions. The authors acknowledge the assistance of NSF of China (Fund Nos. 10871032 and 10871210).

Notes

Communicated by A. Turull.