Some results on the main supergraph of finite groups

• Date: 2021
• Main Authors: Asboei, A. K., Salehi, S. S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2021
• Subjects: graph; main supergraph; finite groups; Thompson's problem; 20D08; 05C25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584
• Journal Title: Algebra and Discrete Mathematics

Let \(G\) be a finite group. The main supergraph \(\mathcal{S}(G)\) is a graph with vertex set \(G\) in which two vertices \(x\) and \(y\) are adjacent if and only if \(o(x) \mid o(y)\) or \(o(y)\mid o(x)\). In this paper, we will show that \(G\cong \mathrm{PSL}(2,p)\) or \(\mathrm{PGL}(2,p)\) if an...