A new characterization of alternating groups

• Date: 2018
• Main Authors: Asboei, Alireza Khalili, Amiri, Syyed Sadegh Salehi, Iranmanesh, Ali
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: finite group; simple group; alternating groups; 20D06; 20D60
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1042
• Journal Title: Algebra and Discrete Mathematics

Let \(G\) be a finite group and let \(\pi_{e}(G)\) be the set of element orders of \(G \). Let \(k \in \pi_{e}(G)\) and let \(m_{k}\) be the number of elements of order \(k \) in \(G\). Set nse(\(G\)):=\(\{ m_{k} | k \in \pi_{e}(G)\}\). In this paper, we show that if \(n = r\), \(r +1 \), \(r + 2\),...