Fitting classes \({\mathcal F}\) such that all finite groups have \({\mathcal F}\)-injectors (Q1087637)

Let \(\mathcal F\) be a homomorph and Fitting class such that \(E_ z\mathcal F=\mathcal F\). The authors prove that if all \(\mathcal F\)-constrained groups have \(\mathcal F\)-injectors, then all groups have \(\mathcal F\)-injectors. In particular if \(\mathcal F\) is a class of quasinilpotent groups containing the nilpotent groups, then every group has \(\mathcal F\)-injectors.