Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (1): 22-24.

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A Note on Theorem of Shlyk

SHI Jiang-tao1, ZHANG Cui2, GUO Song-tao3   

  1. 1.School of Mathematics and Information Science,Yantai University,Yantai Shandong 264005,China;
    2.University of Primorska,IAM,Muzejski trg 2,6000 Koper,Slovenia;
    3.Department of Mathematics,Beijing Jiaotong University,Beijing 100044,China
  • Received:2011-10-11 Online:2012-01-20 Published:2018-12-03

Abstract: The theorem of Shlyk indicates that the intersectionof all nonnormal nonnilpotent maximal subgroups of a finite nonsolvable group isnilpotent.In this paper,a new proof of Shlyk's theorem is given.Moreover,it isproved that the intersection of all nonnilpotent maximal subgroups of a finite nonsolvable group must be equal to its Frattini subgroup.

Key words: finite group, nonnilpotent maximal subgroup, solvablegroup

CLC Number: 

  • O152.1
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