The Average of Some Irreducible Character Degrees

2022/03/23 by Elsharif, Ramadan, Lewis, Mark L.
#20C15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2203.12704

Abstract

We are interested in determining the bound of the average of the degrees of the irreducible characters whose degrees are not divisible by some prime p that guarantees a finite group G of odd order is p-nilpotent. We find a bound that depends on the prime p. If we further restrict our average by fixing a subfield k of the complex numbers and then compute the average of the degrees of the irreducible characters whose degrees are not divisible by p and have values in k, then we will see that we obtain a bound that depends on both p and k. Moreover, we find examples that make those bounds best possible.

Related

• Variations on average character degrees and p-nilpotence
• On the average character degree of finite groups
• On the average character degree of some irreducible characters of a\n finite group
• The average character degree of finite groups and Gluck's conjecture
• Characters of p'-degree and Thompson's character degree theorem