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

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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 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 \({|P/O_p(G)| \leq bcl(G)}\).

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Yong Yang

  2. Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing, 402160, China

    Yong Yang

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  1. Yong Yang
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Correspondence to Yong Yang.

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Yang, Y. The size of the largest conjugacy classes and the Sylow p-subgroups of finite groups. Arch. Math. 108, 9–16 (2017). https://doi.org/10.1007/s00013-016-0978-z

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