Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Group_action> ?p ?o }
- Group_action abstract "In mathematics, a symmetry group is an abstraction used to describe the symmetries of an object. A group action formalizes the relationship between the group and the symmetries of the object. It relates each element of the group to a particular transformation of the object.In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices. It is the same as a group action of G on an ordered basis of a vector space.A group action is an extension to the notion of a symmetry group in which every element of the group \"acts\" like a bijective transformation (or \"symmetry\") of some set, without being identified with that transformation. This allows for a more comprehensive description of the symmetries of an object, such as a polyhedron, by allowing the same group to act on several different sets of features, such as the set of vertices, the set of edges and the set of faces of the polyhedron.If G is a group and X is a set, then a group action may be defined as a group homomorphism h from G to the symmetric group on X. The action assigns a permutation of X to each element of the group in such a way that the permutation of X assigned to the identity element of G is the identity transformation of X; a product gk of two elements of G is the composition of the permutations assigned to g and k.The abstraction provided by group actions is a powerful one, because it allows geometrical ideas to be applied to more abstract objects. Many objects in mathematics have natural group actions defined on them. In particular, groups can act on other groups, or even on themselves. Because of this generality, the theory of group actions contains wide-reaching theorems, such as the orbit stabilizer theorem, which can be used to prove deep results in several fields.".
- Group_action thumbnail Group_action_on_equilateral_triangle.svg?width=300.
- Group_action wikiPageExternalLink tr7abs.html.
- Group_action wikiPageExternalLink topgpds.html.
- Group_action wikiPageID "12781".
- Group_action wikiPageLength "35505".
- Group_action wikiPageOutDegree "171".
- Group_action wikiPageRevisionID "707034809".
- Group_action wikiPageWikiLink 2-transitive_group.
- Group_action wikiPageWikiLink 3-transitive_group.
- Group_action wikiPageWikiLink Abstraction_(mathematics).
- Group_action wikiPageWikiLink Affine_group.
- Group_action wikiPageWikiLink Affine_space.
- Group_action wikiPageWikiLink Algebraic_group.
- Group_action wikiPageWikiLink Algebraic_variety.
- Group_action wikiPageWikiLink Automorphism.
- Group_action wikiPageWikiLink Basis_(linear_algebra).
- Group_action wikiPageWikiLink Bijection.
- Group_action wikiPageWikiLink Burnside_ring.
- Group_action wikiPageWikiLink Burnsides_lemma.
- Group_action wikiPageWikiLink Cartesian_product.
- Group_action wikiPageWikiLink Category:Group_actions.
- Group_action wikiPageWikiLink Category:Group_theory.
- Group_action wikiPageWikiLink Category:Representation_theory_of_groups.
- Group_action wikiPageWikiLink Category:Symmetry.
- Group_action wikiPageWikiLink Category_of_modules.
- Group_action wikiPageWikiLink Category_of_sets.
- Group_action wikiPageWikiLink Category_theory.
- Group_action wikiPageWikiLink Cayleys_theorem.
- Group_action wikiPageWikiLink Classical_mechanics.
- Group_action wikiPageWikiLink Coimage.
- Group_action wikiPageWikiLink Conjugacy_class.
- Group_action wikiPageWikiLink Connected_space.
- Group_action wikiPageWikiLink Continuous_function.
- Group_action wikiPageWikiLink Coset.
- Group_action wikiPageWikiLink Covering_space.
- Group_action wikiPageWikiLink Cross-ratio.
- Group_action wikiPageWikiLink Derived_functor.
- Group_action wikiPageWikiLink Discrete_group.
- Group_action wikiPageWikiLink Discrete_space.
- Group_action wikiPageWikiLink Disjoint_union.
- Group_action wikiPageWikiLink Dynamical_system.
- Group_action wikiPageWikiLink Edge_(geometry).
- Group_action wikiPageWikiLink Empty_set.
- Group_action wikiPageWikiLink Equivalence_class.
- Group_action wikiPageWikiLink Equivalence_relation.
- Group_action wikiPageWikiLink Equivariant_map.
- Group_action wikiPageWikiLink Face_(geometry).
- Group_action wikiPageWikiLink Fibration.
- Group_action wikiPageWikiLink Field_extension.
- Group_action wikiPageWikiLink Finite_geometry.
- Group_action wikiPageWikiLink Function_composition.
- Group_action wikiPageWikiLink Functor.
- Group_action wikiPageWikiLink Fundamental_group.
- Group_action wikiPageWikiLink G-module.
- Group_action wikiPageWikiLink Gain_graph.
- Group_action wikiPageWikiLink Galois_group.
- Group_action wikiPageWikiLink General_linear_group.
- Group_action wikiPageWikiLink Graph_theory.
- Group_action wikiPageWikiLink Group_(mathematics).
- Group_action wikiPageWikiLink Group_action.
- Group_action wikiPageWikiLink Group_cohomology.
- Group_action wikiPageWikiLink Group_homomorphism.
- Group_action wikiPageWikiLink Group_object.
- Group_action wikiPageWikiLink Group_representation.
- Group_action wikiPageWikiLink Group_scheme.
- Group_action wikiPageWikiLink Group_with_operators.
- Group_action wikiPageWikiLink Groupoid.
- Group_action wikiPageWikiLink Identity_element.
- Group_action wikiPageWikiLink Identity_function.
- Group_action wikiPageWikiLink If_and_only_if.
- Group_action wikiPageWikiLink Image_(mathematics).
- Group_action wikiPageWikiLink Inner_automorphism.
- Group_action wikiPageWikiLink Intersection_(set_theory).
- Group_action wikiPageWikiLink Inverse_function.
- Group_action wikiPageWikiLink Isometry.
- Group_action wikiPageWikiLink Isomorphism.
- Group_action wikiPageWikiLink Kernel_(algebra).
- Group_action wikiPageWikiLink Lagranges_theorem_(group_theory).
- Group_action wikiPageWikiLink Lie_group.
- Group_action wikiPageWikiLink Lie_group_action.
- Group_action wikiPageWikiLink Linear_map.
- Group_action wikiPageWikiLink Locally_compact_space.
- Group_action wikiPageWikiLink Manifold.
- Group_action wikiPageWikiLink Mathematics.
- Group_action wikiPageWikiLink Mathieu_group.
- Group_action wikiPageWikiLink Module_(mathematics).
- Group_action wikiPageWikiLink Monoid.
- Group_action wikiPageWikiLink Morphism.
- Group_action wikiPageWikiLink Möbius_transformation.
- Group_action wikiPageWikiLink Natural_transformation.
- Group_action wikiPageWikiLink Neighbourhood_(mathematics).
- Group_action wikiPageWikiLink Normal_subgroup.
- Group_action wikiPageWikiLink Opposite_group.
- Group_action wikiPageWikiLink Orthogonal_group.
- Group_action wikiPageWikiLink Partition_of_a_set.
- Group_action wikiPageWikiLink Pathological_(mathematics).
- Group_action wikiPageWikiLink Permutation.
- Group_action wikiPageWikiLink Permutation_group.
- Group_action wikiPageWikiLink Permutation_matrix.