p-Regular conjugacy classes and p-rational irreducible characters

2020/04/10 by Hung, Nguyen Ngoc, Maroti, Attila · 1 citation
#20C15 #20D05 #20D06 #20D10 #20E45 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2004.05194

Abstract

Let G be a finite group of order divisible by a prime p. The number of p-regular and p'-regular conjugacy classes of G is at least 2√(p-1). Also, the number of p-rational and p'-rational irreducible characters of G is at least 2√(p-1). Along the way we prove a uniform lower bound for the number of p-regular classes in a finite simple group of Lie type in terms of its rank and size of the underlying field.

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