On NSC-groups

A finite p-group G is said to be a NSC-group if all normal subgroups of G which are not contained in Φ(G) have a supplementary subgroup. In this paper we proved some properties of NSC-groups and determined NSC-groups for finite 2-groups, p-groups of nilpotent class 2,3-groups of maximal class, metacyclic p-groups and At-rgroups for t≤ 3.