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On the normal subgroup with coprime G-conjugacy class sizes

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Abstract

Let N be a normal subgroup of a group G. The positive integers m and n are the two longest sizes of the non-central G-conjugacy classes of N with m > n and (m,n) = 1. In this paper, the structure of N is determined when n divides |N/N ∩ Z(G)|. Some known results are generalized.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    XIANHE ZHAO & GUIYUN CHEN

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang Henan, 453007, People’s Republic of China

    XIANHE ZHAO

  3. School of Mathematical Science, Fudan University, Shanghai, 200433, People’s Republic of China

    JIAOYUN SHI

Authors
  1. XIANHE ZHAO
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  2. GUIYUN CHEN
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  3. JIAOYUN SHI
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Correspondence to GUIYUN CHEN.

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ZHAO, X., CHEN, G. & SHI, J. On the normal subgroup with coprime G-conjugacy class sizes. Proc Math Sci 121, 397–404 (2011). https://doi.org/10.1007/s12044-011-0047-2

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  • DOI: https://doi.org/10.1007/s12044-011-0047-2

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