Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Coset> ?p ?o }
- Coset abstract "In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, thengH = { gh : h an element of H } is the left coset of H in G with respect to g, andHg = { hg : h an element of H } is the right coset of H in G with respect to g.Only when H is normal will the set of right cosets and the set of left cosets of H coincide, which is one definition of normality of a subgroup. Although derived from a subgroup, cosets are not usually themselves subgroups of G, only subsets.A coset is a left or right coset of some subgroup in G. Since Hg = g ( g−1Hg ), the right coset Hg (of H with respect to g) and the left coset g ( g−1Hg ) (of the conjugate subgroup g−1Hg ) are the same. Hence it is not meaningful to speak of a coset as being left or right unless one first specifies the underlying subgroup. In other words: a right coset of one subgroup equals a left coset of a different (conjugate) subgroup. If the left cosets and right cosets are the same, then H is a normal subgroup and the cosets form a group called the quotient or factor group.The map gH ↦ (gH)−1 = Hg−1 defines a bijection between the left cosets and the right cosets of H, so the number of left cosets is equal to the number of right cosets. The common value is called the index of H in G.For abelian groups, left cosets and right cosets are always the same. If the group operation is written additively, the notation used changes to g + H or H + g.Cosets are a basic tool in the study of groups; for example they play a central role in Lagrange's theorem.".
- Coset thumbnail Left_cosets_of_Z_2_in_Z_8.svg?width=300.
- Coset wikiPageExternalLink coset.html.
- Coset wikiPageID "98759".
- Coset wikiPageLength "10329".
- Coset wikiPageOutDegree "51".
- Coset wikiPageRevisionID "706587433".
- Coset wikiPageWikiLink Abelian_group.
- Coset wikiPageWikiLink Additive_group.
- Coset wikiPageWikiLink Affine_space.
- Coset wikiPageWikiLink Bijection.
- Coset wikiPageWikiLink Cardinality.
- Coset wikiPageWikiLink Category:Group_theory.
- Coset wikiPageWikiLink Center_(group_theory).
- Coset wikiPageWikiLink Conjugacy_class.
- Coset wikiPageWikiLink Coset_enumeration.
- Coset wikiPageWikiLink Coset_leader.
- Coset wikiPageWikiLink Disjoint_sets.
- Coset wikiPageWikiLink Double_coset.
- Coset wikiPageWikiLink Equivalence_class.
- Coset wikiPageWikiLink Equivalence_relation.
- Coset wikiPageWikiLink Euclidean_space.
- Coset wikiPageWikiLink Euclidean_vector.
- Coset wikiPageWikiLink Group_(mathematics).
- Coset wikiPageWikiLink Heap_(mathematics).
- Coset wikiPageWikiLink Index_of_a_subgroup.
- Coset wikiPageWikiLink Infinity.
- Coset wikiPageWikiLink Lagranges_theorem_(group_theory).
- Coset wikiPageWikiLink Linear_code.
- Coset wikiPageWikiLink Linear_subspace.
- Coset wikiPageWikiLink Mathematics.
- Coset wikiPageWikiLink Modular_arithmetic.
- Coset wikiPageWikiLink Non-measurable_set.
- Coset wikiPageWikiLink Normal_subgroup.
- Coset wikiPageWikiLink Optimal_solutions_for_Rubiks_Cube.
- Coset wikiPageWikiLink Order_(group_theory).
- Coset wikiPageWikiLink Parallel_(geometry).
- Coset wikiPageWikiLink Partition_of_a_set.
- Coset wikiPageWikiLink Quotient_group.
- Coset wikiPageWikiLink Rubiks_Cube.
- Coset wikiPageWikiLink Subgroup.
- Coset wikiPageWikiLink Transfer_(group_theory).
- Coset wikiPageWikiLink Transversal_(combinatorics).
- Coset wikiPageWikiLink Vector_space.
- Coset wikiPageWikiLink Vitali_set.
- Coset wikiPageWikiLink File:Left_cosets_of_Z_2_in_Z_8.svg.
- Coset wikiPageWikiLinkText "Coset".
- Coset wikiPageWikiLinkText "coset".
- Coset wikiPageWikiLinkText "index".
- Coset wikiPageWikiLinkText "left cosets".
- Coset wikiPageWikiLinkText "translates".
- Coset author "Nicolas Bray".
- Coset first "O.A.".
- Coset id "C/c026620".
- Coset last "Ivanova".
- Coset title "Coset in a group".
- Coset title "Coset".
- Coset title "Left Coset".
- Coset title "Right Coset".
- Coset urlname "Coset".
- Coset urlname "LeftCoset".
- Coset urlname "RightCoset".
- Coset wikiPageUsesTemplate Template:Cite_book.
- Coset wikiPageUsesTemplate Template:Cite_web.
- Coset wikiPageUsesTemplate Template:Distinguish.
- Coset wikiPageUsesTemplate Template:Main.
- Coset wikiPageUsesTemplate Template:MathWorld.
- Coset wikiPageUsesTemplate Template:PlanetMath.
- Coset wikiPageUsesTemplate Template:Reflist.
- Coset wikiPageUsesTemplate Template:Springer.
- Coset subject Category:Group_theory.
- Coset hypernym Group.
- Coset type Band.
- Coset type Redirect.
- Coset type Thing.
- Coset comment "In mathematics, if G is a group, and H is a subgroup of G, and g is an element of G, thengH = { gh : h an element of H } is the left coset of H in G with respect to g, andHg = { hg : h an element of H } is the right coset of H in G with respect to g.Only when H is normal will the set of right cosets and the set of left cosets of H coincide, which is one definition of normality of a subgroup.".
- Coset label "Coset".
- Coset differentFrom Cosette.
- Coset sameAs Q751969.
- Coset sameAs مجموعة_مشاركة.
- Coset sameAs Съседен_клас.
- Coset sameAs Classe_lateral.
- Coset sameAs Clase_lateral.
- Coset sameAs هممجموعهها.
- Coset sameAs Sivuluokka.
- Coset sameAs Classe_suivant_un_sous-groupe.
- Coset sameAs מחלקה_(תורת_החבורות).
- Coset sameAs Mellékosztály.
- Coset sameAs Classe_laterale.
- Coset sameAs 剰余類.
- Coset sameAs 잉여류.
- Coset sameAs സഹഗണം.
- Coset sameAs Nevenklasse.
- Coset sameAs Warstwa_(teoria_grup).
- Coset sameAs Coclasse.
- Coset sameAs m.0p8v7.
- Coset sameAs Coset.
- Coset sameAs Sidoklass.
- Coset sameAs இணைக்கணம்.
- Coset sameAs Eşküme.