Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Dedekind_group> ?p ?o. }
Showing items 1 to 24 of
24
with 100 items per page.
- Dedekind_group abstract "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 (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. For instance, he shows "a Hamilton group of order 2a has 22a − 6 quaternion groups as subgroups". In 2005 Horvat et al used this structure to count the number of Hamiltonian groups of any order n = 2eo where o is an odd integer. When e < 3 then there are no Hamiltonian groups of order n, otherwise there are the same number as there are Abelian groups of order o.".
- Dedekind_group wikiPageExternalLink purl?GDZPPN002256258.
- Dedekind_group wikiPageID "153106".
- Dedekind_group wikiPageRevisionID "589269799".
- Dedekind_group hasPhotoCollection Dedekind_group.
- Dedekind_group subject Category:Group_theory.
- Dedekind_group subject Category:Properties_of_groups.
- Dedekind_group comment "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 (Dedekind 1897), proving a form of the above structure theorem (for finite groups). ".
- Dedekind_group label "Dedekind group".
- Dedekind_group label "Groupe hamiltonien (théorie des groupes)".
- Dedekind_group label "Grupa Hamiltona".
- Dedekind_group label "Gruppo hamiltoniano".
- Dedekind_group label "Hamiltoniaanse groep".
- Dedekind_group label "Hamiltonsche Gruppe".
- Dedekind_group sameAs Hamiltonsche_Gruppe.
- Dedekind_group sameAs Groupe_hamiltonien_(théorie_des_groupes).
- Dedekind_group sameAs Gruppo_hamiltoniano.
- Dedekind_group sameAs Hamiltoniaanse_groep.
- Dedekind_group sameAs Grupa_Hamiltona.
- Dedekind_group sameAs m.013zt2.
- Dedekind_group sameAs Q1573561.
- Dedekind_group sameAs Q1573561.
- Dedekind_group wasDerivedFrom Dedekind_group?oldid=589269799.
- Dedekind_group isPrimaryTopicOf Dedekind_group.