Some results on the main supergraph of finite groups

• Дата: 2021
• Автори: Asboei, A. K., Salehi, S. S.
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2021
• Теми: graph; main supergraph; finite groups; Thompson's problem; 20D08; 05C25
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/584
• Назва журналу: 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...