Definitions

Hamiltonian_group

Hamiltonian 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. It can be shown that every Hamiltonian group is a direct product of the form G = Q8 × B × D, where B is the direct sum of some number of copies of the cyclic group C2, and D is a periodic abelian group with all elements of odd order.

Dedekind groups are named after Richard Dedekind, who investigated them in a paper published in 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.

Search another word or see Hamiltonian_groupon Dictionary | Thesaurus |Spanish
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature
FAVORITES
RECENT

;