• $\mathcal M^\ast$-supplemented subgroups of finite groups

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      https://www.ias.ac.in/article/fulltext/pmsc/126/02/0187-0197

    • Keywords

       

      Sylow subgroup; M∗-supplemented subgroups; supersolvable group; formation.

    • Abstract

       

      A subgroup $H$ of a group $G$ is said to be $\mathcal M^\ast$-supplemented in $G$ if there exists a subgroup $K$ of $G$ such that $G = HK$ and $H \cap K$ is $\mathcal M$-supplemented in $G$. In this paper, we prove as follows: Let $E$ be a normal subgroup of a group $G$. Suppose that every maximal subgroup of every non-cyclic Sylow subgroup $P$ of $F^\ast (E)$ is $\mathcal M^\ast$-supplemented in $G$, then $E \leq Z_{\mathcal U\Phi (G)$.

    • Author Affiliations

       

      JIA ZHANG1 LONG MIAO1 JUPING TANG2

      1. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, People’s Republic of China
      2. Wuxi Institute of Technology, Wuxi 214121, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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