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

Abstract

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 followed and some new results are obtained.