\({\mathcal F}\)-constraint with respect to a Fitting class
Let \({\mathcal F}\) be a Fitting class and \(\pi =char {\mathcal F}=\{p|\) \(C_ p\in {\mathcal F}\}\), we say that a group G is \({\mathcal F}\)-constrained when \(C_{\bar G}(\bar G_{{\mathcal F}})\leq G_{{\mathcal F}}\), where \(\bar G=G/O_{\pi '}(G)\). We denote by \({\mathcal X}_{{\mathcal F}}\) the class of \({\mathcal F}\)-constrained groups. In this paper we prove the following results: i) \({\mathcal X}_{{\mathcal F}}\) is a Fitting class. ii) If \({\mathcal N}\subseteq {\mathcal F}\subseteq \tilde N\), then all \({\mathcal X}_{{\mathcal F}}\)-groups possess a unique conjugacy class of \({\mathcal F}\)-injectors. We analyze also the relations between two Fitting classes \({\mathcal F}\) and \({\mathcal H}\) such that \({\mathcal X}_{{\mathcal F}}={\mathcal X}_{{\mathcal H}}\).
conjugacy class of \({\mathcal F}\)-injectors
scientific article; zbMATH DE number 3910601