Saturated Fitting formations (Q1270246)

If \(\mathcal F\) is a saturated and extendable Fitting formation then \(\text{Inj}_{\mathcal F}(G)\) and \(\text{Proj}_{\mathcal F}(G)\) are non empty sets [\textit{M. J. Iranzo} and \textit{F. Pérez Monasor}, Publ. Mat., Barc. 32, No. 1, 57-59 (1988; Zbl 0644.20016) and \textit{R. P. Erickson}, Commun. Algebra 10, 1919-1938 (1982; Zbl 0498.20018)]. So it is natural to ask when \(\text{Inj}_{\mathcal F}(G)\cap\text{Proj}_{\mathcal F}(G)\) is a non-empty set. Many questions about Schunck classes can be more readily resolved when translated into questions about the boundaries. In this paper sufficient conditions are obtained for a group \(G\) in the boundary of a saturated and extendable Fitting formation of full characteristic to have \(\mathcal F\)-projectors which are also \(\mathcal F\)-injectors.