有限群共轭类长的一个注记

钱国华;王燕鸣;

数学学报 ›› 2009 ›› Issue (01) : 127-132.

数学学报 ›› 2009 ›› Issue (01) : 127-132. DOI: 10.12386/A2009sxxb0013
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有限群共轭类长的一个注记

    钱国华;王燕鸣;
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A Note on Conjugacy Class Sizes in Finite Groups

    Guo Hua QIAN Department of Mathematics,Changshu Institute of Technology,Changshu 215500,P.R.China;School of Mathematics,Zhongshan University,Guangzhou 510275,P.R.China Yan Ming WANG Lingnan College and School of Mathematics,Zhongshan University,Guangzhou
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摘要

设G是一个有限群,p是一素数.本文证明了下面的结论:若对每个P-正则元x∈G,p~2不整除类长|x~G|,则对G的每个主因子M/N,都有|M/N|_p=1或p,从而推广或加强了一些已知的有趣结果.

Abstract

Let G be a finite group and p be a prime.It is shown that if p~2 does not divide|x~G|for every p-regular element x∈G,then|M/N|_p=1 or p for any chief factor M/N of G.And then some interesting known results are generalized or strengthened.

关键词

有限群 / p-秩 / 共轭类长

Key words

conjugacy class sizes / finite group / p-rank

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钱国华;王燕鸣;. 有限群共轭类长的一个注记. 数学学报, 2009(01): 127-132 https://doi.org/10.12386/A2009sxxb0013
Guo Hua QIAN Department of Mathematics,Changshu Institute of Technology,Changshu 215500,P.R.China;School of Mathematics,Zhongshan University,Guangzhou 510275,P.R.China Yan Ming WANG Lingnan College and School of Mathematics,Zhongshan University,Guangzhou. A Note on Conjugacy Class Sizes in Finite Groups. Acta Mathematica Sinica, Chinese Series, 2009(01): 127-132 https://doi.org/10.12386/A2009sxxb0013

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