Codegrees and element orders of almost simple groups

Abstract

G. Qian proposed a conjecture which states that if an element of a finite group G has order a, then there exists an irreducible character of codegree b of G such that a divides b. He showed that the conjecture holds for solvable groups. In this note, we settle the conjecture for almost simple groups.

Keyword:

• Almost simple groups
• codegrees
• element orders

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20C15

Acknowledgments

The author would like to thank the reviewer for the careful reading of the article.