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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The authors deeply thank the referee for carefully reading the original manuscript and making some corrections.
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Communicated by J. S. Wilson.
Y. Liu and X. Song were partially supported by the National 973 Project (452101650122) and the National Natural Science Foundation of China (11201194).
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Liu, Y., Song, X. On the largest conjugacy class length of a finite group. Monatsh Math 174, 259–264 (2014). https://doi.org/10.1007/s00605-013-0511-4
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DOI: https://doi.org/10.1007/s00605-013-0511-4