Journal of Guangxi Normal University(Natural Science Edition) ›› 2020, Vol. 38 ›› Issue (4): 54-58.doi: 10.16088/j.issn.1001-6600.2020.04.006

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On Generalized c#-subgroups of Finite Groups

WEI Huaquan1*, YUAN Weifeng1, ZHOU Yuzhen2, LI Xue1, LI Min1   

  1. 1. College of Mathematics and Information Science, Guangxi University, Nanning Guangxi 530004, China;
    2. Dean's Office, Guangxi University, Nanning Guangxi 530004, China
  • Received:2019-04-25 Published:2020-07-13

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Abstract: A subgroup H of a finite group G is said to be a generalized c#-normal subgroup of G if there exists a normal subgroup K of G such that HK is normal in G and H∩K is a CAP-subgroup of G. By using the c#-normality of some Hall and maximal subgroups, several sufficient or necessary conditions are obtained for a group to be π-solvable or solvable.

Key words: finite group, generalized c#-normal subgroup, Hall subgroup, solvable group

CLC Number: 

  • O152.1
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