On generalized covering subgroups and normalizers of finite soluble groups (Q1071862)

If \(G\) is a finite soluble group, \(P\) a superpronormal subgroup of \(G\) and \(\mathfrak H\) is a Schunck class of the form \(\mathfrak H=E_{\Phi}\mathfrak F\) for some formation \(\mathfrak F\), a new conjugacy class of subgroups, namely the \((P,\mathfrak H)\)-normalizers of \(G\), is introduced, extending the results of Carter-Hawkes and Mann on normalizers. We investigate this conjugacy class of subgroups and its relations with the \((P,\mathfrak H)\)-covering subgroups introduced by Fischer and studied by \textit{U. Herzfeld} [Arch. Math. 41, 404--409 (1983; Zbl 0506.20005)].