No abstract

No abstract

No abstract

A group G is called Dedekindian if every subgroup ofG is normal in G.The structure of the finite Dedekindian groups is well-known [3, Satz 7.12]. They are either abelian or direct products of the form Q × A × B, where Q is the quaternion group of order 8, Ais abelian of odd order and exp(B) ≤ 2.

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 pgroups 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.