On generalizations of baer’s theorems about the hypercenter of a finite group

Abstract

We investigate the intersection of normalizers and F-subnormalizers of different types of systems of subgroups (F-maximal, Sylow, cyclic primary). We described all formations F = × i∈I Fπi for which the intersection of normalizers of all Fi-maximal subgroups of G is the Fhypercenter of G for every group G. Also we described all formations F for which the intersection of F-subnormalizers of all Sylow (cyclic primary) subgroups of G is the F-hypercenter of G for every group G.