Structure of locally graded CDN[)-groups

Abstract

We introduce the notion of CDN[)-groups:G is a CDN[)-group if, for any pair of its subgroupsA andB such thatA is a proper nonmaximum subgroup, ofB, there exists a normal subgroupN which belongs toG and satisfies the inequalitiesA≤N. Fifteen types of nilpotent non-Dedekind groups and nine types of nonnilpotent locally graded groups of this kind are obtained.