The influence of minimal p-subgroups on the structure of finite groups (Q802010)

If the center of a finite group G contains the minimal p-subgroups of G (i.e., the elements of order 1, p and 4 when \(p=2)\) then, by a classical result of N. Ito, \(G/O_{p'}(G)\) is a p-group. In this paper it is shown that if K is a normal subgroup of G such that (i) G/K is in a saturated formation F and (ii) the minimal p-subgroups of K lie in the F- hypercenter of G then \(G/O_{p'}(G)\) is in F.