Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Symmetric_group> ?p ?o }
- Symmetric_group abstract "In abstract algebra, the symmetric group Sn on a finite set of n symbols is the group whose elements are all the permutation operations that can be performed on n distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself. Since there are n! (n factorial) possible permutation operations that can be performed on a tuple composed of n symbols, it follows that the order (the number of elements) of the symmetric group Sn is n!.Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory. For the remainder of this article, "symmetric group" will mean a symmetric group on a finite set.The symmetric group is important to diverse areas of mathematics such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G is isomorphic to a subgroup of the symmetric group on G.".
- Symmetric_group thumbnail Symmetric_group_4;_Cayley_graph_4,9.svg?width=300.
- Symmetric_group wikiPageExternalLink fm28128.pdf.
- Symmetric_group wikiPageExternalLink item?id=ASENS_1948_3_65__239_0.
- Symmetric_group wikiPageExternalLink search?q=Symmetric+Group.
- Symmetric_group wikiPageExternalLink marcus_du_sautoy_symmetry_reality_s_riddle.html.
- Symmetric_group wikiPageID "28901".
- Symmetric_group wikiPageLength "39258".
- Symmetric_group wikiPageOutDegree "199".
- Symmetric_group wikiPageRevisionID "683533684".
- Symmetric_group wikiPageWikiLink Abelian_group.
- Symmetric_group wikiPageWikiLink Abelianization.
- Symmetric_group wikiPageWikiLink Abel–Ruffini_theorem.
- Symmetric_group wikiPageWikiLink Abstract_algebra.
- Symmetric_group wikiPageWikiLink Adjacent_transposition.
- Symmetric_group wikiPageWikiLink Affine_general_linear_group.
- Symmetric_group wikiPageWikiLink Affine_group.
- Symmetric_group wikiPageWikiLink Almost_simple_group.
- Symmetric_group wikiPageWikiLink Alternating_group.
- Symmetric_group wikiPageWikiLink Annals_of_Mathematics.
- Symmetric_group wikiPageWikiLink Augustin-Louis_Cauchy.
- Symmetric_group wikiPageWikiLink Automorphism.
- Symmetric_group wikiPageWikiLink Automorphism_group.
- Symmetric_group wikiPageWikiLink Automorphisms_of_the_symmetric_and_alternating_groups.
- Symmetric_group wikiPageWikiLink Bijection.
- Symmetric_group wikiPageWikiLink Braid_group.
- Symmetric_group wikiPageWikiLink Bruhat_order.
- Symmetric_group wikiPageWikiLink Bubble_sort.
- Symmetric_group wikiPageWikiLink Cambridge_University_Press.
- Symmetric_group wikiPageWikiLink Category:Finite_reflection_groups.
- Symmetric_group wikiPageWikiLink Category:Permutation_groups.
- Symmetric_group wikiPageWikiLink Category:Symmetry.
- Symmetric_group wikiPageWikiLink Cayleys_theorem.
- Symmetric_group wikiPageWikiLink Center_(group_theory).
- Symmetric_group wikiPageWikiLink Centralizer_and_normalizer.
- Symmetric_group wikiPageWikiLink Characteristic_(algebra).
- Symmetric_group wikiPageWikiLink Characteristic_subgroup.
- Symmetric_group wikiPageWikiLink Classification_of_finite_simple_groups.
- Symmetric_group wikiPageWikiLink Clifford_algebra.
- Symmetric_group wikiPageWikiLink Combinatorics.
- Symmetric_group wikiPageWikiLink Commutative_property.
- Symmetric_group wikiPageWikiLink Commutator_subgroup.
- Symmetric_group wikiPageWikiLink Complete_group.
- Symmetric_group wikiPageWikiLink Complex_number.
- Symmetric_group wikiPageWikiLink Conjugacy_class.
- Symmetric_group wikiPageWikiLink Covering_groups_of_the_alternating_and_symmetric_groups.
- Symmetric_group wikiPageWikiLink Coxeter_group.
- Symmetric_group wikiPageWikiLink Crelles_Journal.
- Symmetric_group wikiPageWikiLink Cube.
- Symmetric_group wikiPageWikiLink Cubic_function.
- Symmetric_group wikiPageWikiLink Cubic_polynomial.
- Symmetric_group wikiPageWikiLink Cyclic_group.
- Symmetric_group wikiPageWikiLink Cyclic_permutation.
- Symmetric_group wikiPageWikiLink Dihedral_group_of_order_6.
- Symmetric_group wikiPageWikiLink Dihedral_group_of_order_8.
- Symmetric_group wikiPageWikiLink Dimension_(vector_space).
- Symmetric_group wikiPageWikiLink Discrete_Fourier_transform.
- Symmetric_group wikiPageWikiLink Dover_Publications.
- Symmetric_group wikiPageWikiLink Empty_function.
- Symmetric_group wikiPageWikiLink Empty_set.
- Symmetric_group wikiPageWikiLink Equilateral_triangle.
- Symmetric_group wikiPageWikiLink Even_and_odd_permutations.
- Symmetric_group wikiPageWikiLink Examples_of_groups.
- Symmetric_group wikiPageWikiLink Exceptional_object.
- Symmetric_group wikiPageWikiLink Factorial.
- Symmetric_group wikiPageWikiLink Field_(mathematics).
- Symmetric_group wikiPageWikiLink Field_extension.
- Symmetric_group wikiPageWikiLink Finite_extension.
- Symmetric_group wikiPageWikiLink Finite_set.
- Symmetric_group wikiPageWikiLink Finitely_presented_group.
- Symmetric_group wikiPageWikiLink Frobenius_group.
- Symmetric_group wikiPageWikiLink Function_composition.
- Symmetric_group wikiPageWikiLink Galois_extension.
- Symmetric_group wikiPageWikiLink Galois_group.
- Symmetric_group wikiPageWikiLink Galois_theory.
- Symmetric_group wikiPageWikiLink General_linear_group.
- Symmetric_group wikiPageWikiLink Generalized_symmetric_group.
- Symmetric_group wikiPageWikiLink Gerolamo_Cardano.
- Symmetric_group wikiPageWikiLink Graph_(mathematics).
- Symmetric_group wikiPageWikiLink Group_(mathematics).
- Symmetric_group wikiPageWikiLink Group_action.
- Symmetric_group wikiPageWikiLink Group_algebra.
- Symmetric_group wikiPageWikiLink Group_cohomology.
- Symmetric_group wikiPageWikiLink Group_homology.
- Symmetric_group wikiPageWikiLink Group_homomorphism.
- Symmetric_group wikiPageWikiLink Group_isomorphism.
- Symmetric_group wikiPageWikiLink Group_operation.
- Symmetric_group wikiPageWikiLink Group_representation.
- Symmetric_group wikiPageWikiLink Group_theory.
- Symmetric_group wikiPageWikiLink Higman–Sims_graph.
- Symmetric_group wikiPageWikiLink Higman–Sims_group.
- Symmetric_group wikiPageWikiLink History_of_group_theory.
- Symmetric_group wikiPageWikiLink Homogeneous_space.
- Symmetric_group wikiPageWikiLink Hopf_algebra.
- Symmetric_group wikiPageWikiLink Hyperoctahedral_group.
- Symmetric_group wikiPageWikiLink Icosahedral_group.
- Symmetric_group wikiPageWikiLink Icosahedral_symmetry.
- Symmetric_group wikiPageWikiLink Identical_particles.
- Symmetric_group wikiPageWikiLink Identity_element.
- Symmetric_group wikiPageWikiLink Inner_automorphism.