JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 98-102.doi: 10.6040/j.issn.1671-9352.0.2023.047

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Influence of $\mathscr{F}$-supplemented property of maximal subgroups of Sylow p-subgroup on the structure of groups

Baijun GAO1(),Juping TANG2,Zhichao GAO3,*(),Ju SONG4   

  1. 1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
    2. Department of Fundamental Courses, Wuxi Institute of Technology, Wuxi 214121, Jiangsu, China
    3. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China
    4. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, Jiangsu, China
  • Received:2023-02-14 Online:2024-06-20 Published:2024-06-17
  • Contact: Zhichao GAO E-mail:dqgbj2008@163.com;1102576920@qq.com

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Abstract:

Using the theory of group classes, the group classes $S_{p^{2}}^{*}$ and $S_{p^{3}}^{*}$ are obtained by generalizing the group class $S_{p}^{*}$, and $S_{p^i}^{*}$-supplemented subgroups are defined, where $i=1, 2, 3$. Furthermore, the structure of generalized $p$-solvable groups is studied by using $S_{p^{i}}^{*}$-supplemented property of maximal subgroups of Sylow $p$-subgroup.

Key words: Sylow p-subgroup, maximal subgroup, supplemented subgroup, generalized p-solvable group

CLC Number: 

  • O152.1
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