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    • Keywords


      Frattini chief factors; solvable groups; semi cover-avoiding properties.

    • Abstract


      A subgroup 𝐻 of a group 𝐺 is said to be a semi $CAP^∗$-subgroup of 𝐺 if there is a chief series $1 = G_0$ < $G_1$ <$\cdots$ < $G_m = G$ of 𝐺 such that for every non-Frattini chief factor $G_i/G_{i-1},H$ either covers $G_i/G_{i-1}$ or avoids $G_i/G_{i-1}$. In this paper, some sufficient conditions for a normal subgroup of a finite group to be solvable are given based on the assumption that some maximal subgroups are semi $CAP^∗$-subgroups.

    • Author Affiliations


      Jianjun Liu1 Xiuyun Guo2 Qianlu Li3

      1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
      2. Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
      3. Department of Mathematics, Shanxi Datong University, Datong, Shanxi 037009, People’s Republic of China
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

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