Finite groups with one incidence condition connected with the inversion of Lagrange’s the-orem. Part 1

One class of finite groups in which for noncyclic subgroups one of the inversions of La-grange’s theorem holds true (Ln-groups) is described in this paper. In the part 1, nilpotent Ln-groups are described and several properties of non-nilpotent Ln-groups are established.