Some Results on the \({\cal F}{\rm{\Phi }}\)-Hypercenter of Finite Groups

Abstract

Asubgroup H of G is said to be \({{\cal M}_p}\)-supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H with ∣H: T∣ = p^α. In this paper, we will investigate the structure of \({Z_{{\cal F}\Phi }}\left( G \right)\) by using \({{\cal M}_p}\)-supplemented subgroups.