A note on finite groups generated by their subnormal subgroups (Q2747931)

Following the theory of operators created by \textit{H. Wielandt} [Subnormale Untergruppen endlicher Gruppen, Vorlesung (Univ. Tübingen, 1971), Mathematical works. Vol. I, de Gruyter (1994; Zbl 0802.20001), pp. 412-479], the authors ask for what kind of formations \(\mathcal F\) and for what kind of subnormal subgroups \(U\) and \(V\) of a finite group \(G\) we have that the \(\mathcal F\)-residual of the subgroup generated by two subnormal subgroups of a group is the subgroup generated by the \(\mathcal F\)-residuals of the subgroups. In this paper the authors provide an answer whenever \(U\) is quasinilpotent and \(\mathcal F\) is either a Fitting formation or a saturated formation closed for quasinilpotent subnormal subgroups.