Journal of Guangxi Normal University(Natural Science Edition) ›› 2015, Vol. 33 ›› Issue (4): 63-67.doi: 10.16088/j.issn.1001-6600.2015.04.011

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NS*-quasinormal Subgroups and p-nilpotency of Finite Groups

XIANG Rong1, WU Yong2, ZHONG Xiang-gui1   

  1. 1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China;
    2. College of Information Technology, Guilin University of Electronic Technology, Guilin Guangxi 541004, China
  • Received:2015-05-04 Online:2015-12-25 Published:2018-09-21

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Abstract: Let G be a finite group. A subgroup H of G is said to be an NS-quasinormal subgroup of G if for every prime p such that (p,|H|)=1 and for every subgroup L of G containing H, the normalizer NL(H) contains some Sylow p-subgroup of L. A subgroup H of G is said to be an NS*-quasinormal subgroup of G if G has a normal subgroup K such that G=HK, and H∩K is an NS-subgroup of G. In this paper, by using NS*-quasinormal subgroups of order p or p2, some sufficient conditions for G to be p-nilpotent are obtained.

Key words: finite group, NS*-quasinormal subgroup, p-nilpotent group

CLC Number: 

  • O152.1
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