On The Largest Character Degree And Solvable Subgroups Of Finite Groups

2024/10/10 by Wu, Zongshu, Yang, Yong
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.07556

Abstract

Let G be a finite group, and π be a set of primes. The π-core O_π(G) is the unique maximal normal π-subgroup of G, and b(G) is the largest irreducible character degree of G. In 2017, Qian and Yang proved that if H is a solvable π-subgroup of G, then |HO_π(G)/O_π(G)|≤ b(G)³. In this paper, we improve the exponent of 3 to 3log₅₀₄(168)<2.471.

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