FACTOID # 11: Oklahoma has the highest rate of women in State or Federal correctional facilities.
 
 Home   Encyclopedia   Statistics   States A-Z   Flags   Maps   FAQ   About 
   
 
WHAT'S NEW
 

SEARCH ALL

FACTS & STATISTICS    Advanced view

Search encyclopedia, statistics and forums:

 

 

(* = Graphable)

 

 


Encyclopedia > Hamiltonian group

In group theory, a non-abelian group G is called Hamiltonian if every subgroup of G is normal.


Clearly, every abelian group has this property, because all subgroups of an abelian group are normal subgroups, but there are non-abelian examples as well. The most familiar (and smallest) is the quaternion group of order 8, denoted by Q8.


It can be shown that every Hamiltonian group is a direct sum 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.


  Results from FactBites:
 
Faculty groups at CUNY (552 words)
Many faculty participate in more than one research group.
Anshel, Michael: combinatorial group theory and its relationship to computational complexity, cryptography and number theory
Osin, Denis: Geometric group theory; Coarse geometry; Algebraic topology.
Quaternion group - Wikipedia, the free encyclopedia (480 words)
The inner automorphism group of Q is isomorphic to Q modulo its center, and is therefore also isomorphic to the Klein four-group.
The quaternion group Q may be regarded as acting on the eight nonzero elements of the 2-dimensional vector space over the finite field GF(3).
The generalized quaternion groups are members of the still larger family of dicyclic groups.
  More results at FactBites »

 
 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments

Want to know more?
Search encyclopedia, statistics and forums:

 


Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m