Journal of Guangxi Normal University(Natural Science Edition) ›› 2014, Vol. 32 ›› Issue (3): 52-56.

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Finite Non-solvable Groups with a Small Number of Conjugacy Classes of Non-trivial Cyclic Subgroups

SHI Jiang-tao, ZHANG Cui   

  1. School of Mathematics and Information Science, Yantai University, Yantai Shandong 264005, China
  • Received:2014-02-15 Online:2014-09-25 Published:2018-09-25

Abstract: The structures of finite groups having at most two conjugacy classes of non-trivial cyclic subgroups are completely characterized. It is proven that a finite non-solvable group G having at most four conjugacy classes of non-trivial cyclic subgroups must be isomorphic to PSL2(r), where r=5,7,8,9.

Key words: finite group, cyclic subgroup, non-solvable group

CLC Number: 

  • O152.1
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