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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/04/0511-0516

    • Keywords

       

      $PS$-groups; minimal non-$PS$-groups; supersolvable groups; power automorphisms.

    • Abstract

       

      Let 𝐺 be a finite group. A subgroup 𝐻 of 𝐺 is called 𝑠-permutable in 𝐺 if it permutes with every Sylow subgroup of 𝐺, and 𝐺 is called a $PS$-group if all minimal subgroups and cyclic subgroups with order 4 of 𝐺 are 𝑠-permutable in 𝐺. In this paper, we give a complete classification of finite groups which are not $PS$-groups but their proper subgroups are all $PS$-groups.

    • Author Affiliations

       

      Pengfei Guo1 2 Junxin Wang3 Hailiang Zhang4

      1. School of Mathematics and Information Engineering, Lianyungang Normal College, Lianyungang 222006, People’s Republic of China
      2. Department of Civil and Architectural Engineering, City University of Hong Kong, Hong Kong 999077, People’s Republic of China
      3. Department of Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, People’s Republic of China
      4. Department of Mathematics, Zhejiang Ocean University, Zhoushan 316000, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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