Dedekind group

In group theory, a Dedekind group is a group G such that every subgroup of G is normal. All abelian groups are Dedekind groups. A non-abelian Dedekind group is called a Hamiltonian group.

The most familiar (and smallest) example of a Hamiltonian group is the quaternion group of order 8, denoted by Q₈. Dedekind and Baer have shown (in the finite and respectively infinite order case) that every Hamiltonian group is a direct product of the form G = Q₈ × B × D, where B is an elementary abelian 2-group, and D is a periodic abelian group with all elements of odd order.