On the largest conjugacy class length of a finite group |
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| Authors: | Yanjun Liu Xueling Song |
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| Institution: | 1. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, 330022, China
2. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China
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| Abstract: | Let $G$ be a finite group and $\mathrm{bcl}(G)$ the largest conjugacy class length of $G$ . In this note we slightly improve He and Shi’s lower bound for $\mathrm{bcl}(G)$ , showing that $|\mathrm{bcl}(G)|\ge p^{\frac{1}{p}}(|G:O_{p}(G)|_{p})^{\frac{p-1}{p}}$ . |
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