Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Quotient_group> ?p ?o }
- Quotient_group abstract "In mathematics, specifically group theory, a quotient group (or factor group) is a group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves the group structure. For example, the cyclic group of addition modulo n can be obtained from the integers by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class (known as a congruence class) as a single entity.In a quotient of a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written G / N, where G is the original group and N is the normal subgroup. (This is pronounced "G mod N," where "mod" is short for modulo.)Much of the importance of quotient groups is derived from their relation to homomorphisms. The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G. Specifically, the image of G under a homomorphism φ: G → H is isomorphic to G / ker(φ) where ker(φ) denotes the kernel of φ.The dual notion of a quotient group is a subgroup, these being the two primary ways of forming a smaller group from a larger one. Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup. In category theory, quotient groups are examples of quotient objects, which are dual to subobjects. For other examples of quotient objects, see quotient ring, quotient space (linear algebra), quotient space (topology), and quotient set.".
- Quotient_group wikiPageID "11526".
- Quotient_group wikiPageLength "14662".
- Quotient_group wikiPageOutDegree "91".
- Quotient_group wikiPageRevisionID "683038213".
- Quotient_group wikiPageWikiLink Abelian_group.
- Quotient_group wikiPageWikiLink Absolute_value.
- Quotient_group wikiPageWikiLink Automorphism.
- Quotient_group wikiPageWikiLink Category:Group_theory.
- Quotient_group wikiPageWikiLink Category_theory.
- Quotient_group wikiPageWikiLink Circle_group.
- Quotient_group wikiPageWikiLink Complex_number.
- Quotient_group wikiPageWikiLink Congruence_class.
- Quotient_group wikiPageWikiLink Conjecture.
- Quotient_group wikiPageWikiLink Correspondence_theorem_(group_theory).
- Quotient_group wikiPageWikiLink Coset.
- Quotient_group wikiPageWikiLink Cyclic_group.
- Quotient_group wikiPageWikiLink Determinant.
- Quotient_group wikiPageWikiLink Differentiable_manifold.
- Quotient_group wikiPageWikiLink Direct_product_of_groups.
- Quotient_group wikiPageWikiLink Division_(mathematics).
- Quotient_group wikiPageWikiLink Dual_(category_theory).
- Quotient_group wikiPageWikiLink Duality_(mathematics).
- Quotient_group wikiPageWikiLink Equivalence_class.
- Quotient_group wikiPageWikiLink Equivalence_relation.
- Quotient_group wikiPageWikiLink Eulers_identity.
- Quotient_group wikiPageWikiLink Exact_sequence.
- Quotient_group wikiPageWikiLink Extension_problem.
- Quotient_group wikiPageWikiLink Fiber_bundle.
- Quotient_group wikiPageWikiLink Fundamental_theorem_on_homomorphisms.
- Quotient_group wikiPageWikiLink Generating_set_of_a_group.
- Quotient_group wikiPageWikiLink Group_(mathematics).
- Quotient_group wikiPageWikiLink Group_extension.
- Quotient_group wikiPageWikiLink Group_homomorphism.
- Quotient_group wikiPageWikiLink Group_isomorphism.
- Quotient_group wikiPageWikiLink Group_order.
- Quotient_group wikiPageWikiLink Group_theory.
- Quotient_group wikiPageWikiLink Homogeneous_space.
- Quotient_group wikiPageWikiLink Identity_element.
- Quotient_group wikiPageWikiLink If_and_only_if.
- Quotient_group wikiPageWikiLink Image_(mathematics).
- Quotient_group wikiPageWikiLink Index_of_a_subgroup.
- Quotient_group wikiPageWikiLink Integer.
- Quotient_group wikiPageWikiLink Isomorphism_theorem.
- Quotient_group wikiPageWikiLink John_Wiley_&_Sons.
- Quotient_group wikiPageWikiLink John_Wiley_and_Sons.
- Quotient_group wikiPageWikiLink Kernel_(algebra).
- Quotient_group wikiPageWikiLink Lattice_theorem.
- Quotient_group wikiPageWikiLink Lie_group.
- Quotient_group wikiPageWikiLink Lie_subgroup.
- Quotient_group wikiPageWikiLink Mathematics.
- Quotient_group wikiPageWikiLink Matrix_(mathematics).
- Quotient_group wikiPageWikiLink Modular_arithmetic.
- Quotient_group wikiPageWikiLink Nilpotent_group.
- Quotient_group wikiPageWikiLink Normal_subgroup.
- Quotient_group wikiPageWikiLink Order_(group_theory).
- Quotient_group wikiPageWikiLink Orthogonal_group.
- Quotient_group wikiPageWikiLink Paillier_cryptosystem.
- Quotient_group wikiPageWikiLink Pallier_cryptosystem.
- Quotient_group wikiPageWikiLink Principal_bundle.
- Quotient_group wikiPageWikiLink Quotient_category.
- Quotient_group wikiPageWikiLink Quotient_object.
- Quotient_group wikiPageWikiLink Quotient_ring.
- Quotient_group wikiPageWikiLink Quotient_set.
- Quotient_group wikiPageWikiLink Quotient_space_(linear_algebra).
- Quotient_group wikiPageWikiLink Quotient_space_(topology).
- Quotient_group wikiPageWikiLink Real_number.
- Quotient_group wikiPageWikiLink Root_of_unity.
- Quotient_group wikiPageWikiLink Roots_of_unity.
- Quotient_group wikiPageWikiLink Rotation.
- Quotient_group wikiPageWikiLink Semidirect_product.
- Quotient_group wikiPageWikiLink Short_exact_sequence.
- Quotient_group wikiPageWikiLink Solvable_group.
- Quotient_group wikiPageWikiLink Subgroup.
- Quotient_group wikiPageWikiLink Subobject.
- Quotient_group wikiPageWikiLink Surjective.
- Quotient_group wikiPageWikiLink Surjective_function.
- Quotient_group wikiPageWikiLink Trivial_(mathematics).
- Quotient_group wikiPageWikiLink Triviality_(mathematics).
- Quotient_group wikiPageWikiLink Unit_circle.
- Quotient_group wikiPageWikiLink File:Normal_subgroup_illustration.svg.
- Quotient_group wikiPageWikiLinkText "''quotient'' or ''factor'' group".
- Quotient_group wikiPageWikiLinkText "/".
- Quotient_group wikiPageWikiLinkText "Quotient group".
- Quotient_group wikiPageWikiLinkText "R/Z".
- Quotient_group wikiPageWikiLinkText "canonical projection".
- Quotient_group wikiPageWikiLinkText "complementary (quotient) group".
- Quotient_group wikiPageWikiLinkText "factor group".
- Quotient_group wikiPageWikiLinkText "factoring".
- Quotient_group wikiPageWikiLinkText "groups".
- Quotient_group wikiPageWikiLinkText "modulo".
- Quotient_group wikiPageWikiLinkText "quotient group".
- Quotient_group wikiPageWikiLinkText "quotient map".
- Quotient_group wikiPageWikiLinkText "quotient".
- Quotient_group wikiPageWikiLinkText "quotients".
- Quotient_group hasPhotoCollection Quotient_group.
- Quotient_group wikiPageUsesTemplate Template:!.
- Quotient_group wikiPageUsesTemplate Template:Citation.
- Quotient_group wikiPageUsesTemplate Template:Group_theory_sidebar.
- Quotient_group wikiPageUsesTemplate Template:Reflist.