Mutually permutable products of finite groups. II
[For Part I see the authors and \textit{M. D. Pérez-Ramos}, ibid. 213, No. 1, 369-377 (1999; Zbl 0917.20020).] The finite group \(G=HK\) is the mutually permutable product of its subgroups \(H\) and \(K\) if \(H\) permutes with every subgroup of \(K\) and \(K\) permutes with every subgroup of \(H\). The following theorem is proved. Let \(\mathcal F\) be a saturated formation containing the class of supersoluble groups. If the commutator subgroup of \(G\) is nilpotent, then the \(\mathcal F\)-residual \(G^{\mathcal F}\) of the mutually permutable product \(G=HK\) can be written as \(G^{\mathcal F}=H^{\mathcal F}K^{\mathcal F}\). However, an easy example shows that an \(\mathcal F\)-projector of \(G\) in general cannot be obtained from the corresponding projectors of the factor subgroups.
scientific article; zbMATH DE number 1348172