Journal of Guangxi Normal University(Natural Science Edition) ›› 2017, Vol. 35 ›› Issue (1): 44-48.doi: 10.16088/j.issn.1001-6600.2017.01.007

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Influence of the Number of Conjugacy Classes of Nonsubnormal Subgroups on the Structure of Finite Groups

ZHONG Xianggui, DING Ruifang, LING Simin   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Online:2017-01-20 Published:2018-07-17

Abstract: Let G be a finite group, π(G) be the set of prime factors dividing |G| and μ(G) denote the number of conjugacy classes of all non-subnormal subgroups of G. In this paper, it is shown that all finite groups G with μ(G)≤2|π(G)| are solvable and that the structure of finite groups having at most |π(G)| conjugacy classes of non-subnormal subgroups are completely characterized.

Key words: finite group, subnormal subgroup, conjugacy class, solvable groups

CLC Number: 

  • O152.1
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