2-Groups with normal noncyclic subgroups

We study nearly-hamiltonian 2-groups (¯H₂-groups). A nonabelian 2-group having at least one proper noncyclic subgroup is called an ¯H₂-group if all noncyclic subgroups are normal.Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 75–84, July, 1968.The author expresses his deep gratitude towards Professor S. N. Chernikov for guidance while writing this paper.