• Finite groups all of whose minimal subgroups are $NE^{\ast}$-subgroups

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/124/04/0501-0509

    • Keywords

       

      $NE$-subgroup; $NE^{\ast}$-subgroup; the generalized fitting subgroup; saturated formation.

    • Abstract

       

      Let 𝐺 be a finite group. A subgroup 𝐻 of 𝐺 is called an $NE$-subgroup of 𝐺 if it satisfies $H^G \cap N_{G}(H) = H$. A subgroup 𝐻 of 𝐺 is said to be a $NE^{\ast}$-subgroup of 𝐺 if there exists a subnormal subgroup 𝑇 of 𝐺 such that $G = HT$ and $H \cap T$ is a $NE$-subgroup of 𝐺. In this article, we investigate the structure of 𝐺 under the assumption that subgroups of prime order are $NE^{\ast}$-subgroups of 𝐺. The finite groups, all of whose minimal subgroups of the generalized Fitting subgroup are $NE^{\ast}$-subgroups are classified.

    • Author Affiliations

       

      Yonggang Li1 Xianggui Zhong2

      1. Lijiang College of Guangxi Normal University, Guangxi, Guilin 541006, People’s Republic of China
      2. Department of Mathematics, Guangxi Normal University, Guangxi, Guilin 541004, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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