• Finite Groups with the Set of the Number of Subgroups of Possible Order Containing Exactly Two Elements

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      https://www.ias.ac.in/article/fulltext/pmsc/123/04/0491-0498

    • Keywords

       

      Finite group; the number of subgroups of possible order.

    • Abstract

       

      Let 𝐺 be a finite group, and $n(G)$ be the set of the number of subgroups of possible order of 𝐺. We investigate the structure of 𝐺 satisfying that $n(G) = \{1, m\}$ for any positive integer 𝑚 > 1. At first, we prove that the nilpotent length of 𝐺 is less than 2. Secondly, we investigate nilpotent groups with $m = p + 1$ or $p^2 + p + 1$ (𝑝 is a prime), and we get the classification of such kinds of groups. At last, we investigate non-nilpotent groups with $m = p + 1$ and get the classification of the groups under consideration.

    • Author Affiliations

       

      Yanheng Chen1 2 Guiyun Chen1

      1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
      2. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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