JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 15-19, 27.doi: 10.6040/j.issn.1671-9352.0.2023.404

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Influence of second maximal subgroups with given properties on structure of groups

Xiaohong ZHANG1(),Wei LIU2,Hongzhi WANG3   

  1. 1. School of Statistics and Data Science, Ningbo University of Technology, Ningbo 315211, Zhejiang, China
    2. College of Mathematical Science, Yangzhou University, Yangzhou 225002, Jiangsu, China
    3. School of Mathematics, Hohai University, Nanjing 210098, Jiangsu, China
  • Received:2023-09-18 Online:2024-08-20 Published:2024-07-31

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Abstract:

A subgroup A of a finite group G is said to be NS-supplemented in G, if there exists a subgroup B of G such that G=AB and whenever X is a normal subgroup of A and p∈π(B). There exists a Sylow p-subgroup Bp of B, such that XBp=BpX. In this paper, we explore the structure of finite groups by utilizing the properties of NS-supplement and cover-avoidance of second maximal subgroups in specific sets, and characterize the related classes of groups.

Key words: maximal subgroup, second maximal subgroup, cover-avoidance property, NS-supplement, class of group

CLC Number: 

  • O152.1
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