A criterion for the locality of formation products (Q788106)

All considerations of this paper are concerned with subclasses of a class of groups \({\mathfrak U}\) which is closed with respect to S, Q, and \(Ext_{{\mathfrak A}}\). The class of all \(\pi\)-groups in \({\mathfrak U}\) is denoted by \({\mathfrak U}_{\pi}\). Suppose now that \({\mathfrak F}\) is a local formation and \({\mathfrak H}\) is an arbitrary formation, following Shemetkov the formation of all groups with \({\mathfrak F}\)-projectors in \({\mathfrak H}\) is denoted by \({\mathfrak F}*_ 2{\mathfrak H}\). For the case \({\mathfrak F}={\mathfrak U}_{\pi}\) conditions are given such that \({\mathfrak F}*_ 2{\mathfrak H}\) is local. This generalizes a result of Blessenohl.