On \(\frak{F}\)-radicals of finite \(\pi\)-soluble groups

• Main Authors: Guo, Wenbin, Liu, Xi, Li, Baojun
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Finite group; \(\pi\)-soluble group; \({\cal F}\)-radical; Fitting class; 20D10; 20D25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/897

In this paper, we prove that for every local \(\pi\)-saturated Fitting class \({\cal F}\) with \(char ({\cal F})=\mathbb{P}\), the \({\cal F}\)-radical of every finite \(\pi\)-soluble groups \(G\) has the property: \(C_G(G_{\cal F})\subseteq G_{\cal F}\). From this, some well known results are follo...