Abelian subgroups, nilpotent subgroups, and the largest character degree of a finite group

2019/05/25 by Hung, Nguyen Ngoc, Yang, Yong
#20D10 #20D15 #FOS: Mathematics #Group Theory (math.GR) #Primary 20C15 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1905.10512

Abstract

Let H be an abelian subgroup of a finite group G and π the set of prime divisors of |H|. We prove that |H O_π(G)/ O_π(G)| is bounded above by the largest character degree of G. A similar result is obtained when H is nilpotent.

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