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

Research paper by Guohua Qian, Yong Yang

Indexed on: 04 Oct '17Published on: 04 Oct '17Published in: arXiv - Mathematics - Group Theory



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.