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

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    • 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



      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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