Finite equilibrated 2-generated 2-groups

A group is called equilibrated if no subgroup H of G can be written as a product of two non- normal subgroups of H. Blackburn, Deaconescu and Mann [ 1] investigated the finite equilibrated groups, giving a complete description of the non- soluble ones. On the other hand, they showed that the property of a finite nilpotent group of being equilibrated depends solely on the structure of its 2- generated p- subgroups. Consequently, all the finite 2- generated equilibrated p-groups were classified for any odd prime p, but the case p = 2 remained unsolved. This special case will represent the subject of the present paper.