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

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 2
April 2019