Structure of locally graded CDN (]-groups

We introduce the notion of a CDN(]-group G, namely, a group such that, for any pair of its subgroups A and B such that A is a proper nonmaximal subgroup of B, there exists a normal subgroup N of G and A < N ≤ B. Thirteen types of non-Dedekind nilpotent groups and 9 types of nonnilpotent locally graded groups of this kind are described. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1532–1536, November, 1998.