Dedekind group

In group theory, a group is called Dedekind group ( according to R. Dedekind ) if every subgroup is a normal subgroup. Apparently, every abelian group is a Dedekind group. The non- abelian among them are called ( by WR Hamilton) Hamilton groups.

The Hamiltonian groups can be fully specified by a going back to R. Dedekind set:

• Each finite Hamiltonian group is of the form, wherein   the quaternion group is
• An abelian group of odd order is
• And is.

If so, the third factor is missing. The group may be a singleton, then the second factor is missing. The quaternion group is therefore the smallest Hamiltonian group and each group contains an isomorphic Hamiltonian for quaternion subgroup.

Accordingly, and no Hamiltonian groups. In fact, are non-normal or sub-groups, it being usual and.