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arXiv · 1710.01861

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

Guohua Qian·Yong Yang
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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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Guohua Qian, Yong Yang. 2017-10-05. The largest size of conjugacy class and the $p$-parts of finite groups. https://arxiv.org/abs/1710.01861

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