On \(\pi\)-normally embedded subgroups of finite soluble groups
The authors consider the following condition where \(\pi\) is a set of primes: A subgroup \(H\) of a group \(G\) is said to be \(\pi\)-normally embedded if a Hall \(\pi\)-subgroup of \(H\) is a Hall \(\pi\) subgroup of some normal subgroup of \(G\). This generalizes the concept of \(p\)-normally embedded subgroups which is the case when \(\pi=\{p\}\). In this very nice paper a number of results for \(p\)-normally embedded subgroups are generalized as appropriate to the situation for \(\pi\)-normally embedded subgroups. As an example here is Theorem 1. Let \(\mathcal F\) be a saturated formation. If \(G\) is a group with Abelian Hall \(\pi\)-subgroups, then \(\mathcal F\)-normalizers of \(G\) are \(\pi\)-normally embedded.
scientific article; zbMATH DE number 1021764