The largest size of conjugacy class and the p-parts of finite groups

2017/10/05 by Guohua Qian, Yong Yang, Qian, Guohua +1
Computer Science · Mathematics · #20D05 #20D20 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1710.01861

openalex publication_date 2017/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime and let P be a Sylow p-subgroup of a finite nonabelian group G. Let bcl(G) be the size of the largest conjugacy class of the group G. We show that |P/O_p(G)| < bcl(G) if G is not abelian.

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