A Generalization of Commutativity Degree of Finite Groups

Abstract

The commutativity degree of a finite group is the probability that two arbitrarily chosen group elements commute. This notion has been generalized in a number of ways. The object of this article is to study yet another generalization of the same notion, which further extends some of the existing generalizations.

Key Words:

• Commutativity degree
• Finite groups
• Group characters

2010 Mathematics Subject Classification:

• 20C15
• 20D60
• 20P05

ACKNOWLEDGMENT

The authors are grateful for the helpful suggestions of the referee.

Notes

Communicated by D. Macpherson.