Dedekind group

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 torsion abelian group with all elements of odd order.

Dedekind groups are named after Richard Dedekind, who investigated them in (Dedekind 1897), proving a form of the above structure theorem (for finite groups).

He named the non-abelian ones after William Rowan Hamilton, the discoverer of quaternions.

In 1898 George Miller delineated the structure of a Hamiltonian group in terms of its order and that of its subgroups.

In 2005 Horvat et al[2] used this structure to count the number of Hamiltonian groups of any order n = 2eo where o is an odd integer.