The size of the largest conjugacy classes and the Sylow p-subgroups of finite groups

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• 作者：Yong Yang
• 关键词：Sylow subgroups ; Conjugacy class size
• 刊名：Archiv der Mathematik
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：108
• 期：1
• 页码：9-16
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1420-8938
• 卷排序：108

文摘

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 classes of the group G. We show that if p is an odd prime but not a Mersenne prime or if P does not involve a section isomorphic to the wreath product \({Z_p \wr Z_p}\), then \({|P/O_p(G)| \leq bcl(G)}\).