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- Outer_automorphism_group abstract "In mathematics, the outer automorphism group of a group Gis the quotient Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted Out(G). If Out(G) is trivial and G has a trivial center, then G is said to be complete.An automorphism of a group which is not inner is called an outer automorphism. Note that the elements of Out(G) are cosets of automorphisms of G, and not themselves automorphisms; this is an instance of the fact that quotients of groups are not in general (isomorphic to) subgroups. Elements of Out(G) are cosets of Inn(G) in Aut(G).For example, for the alternating group An, the outer automorphism group is usually the group of order 2, with exceptions noted below. Considering An as a subgroup of the symmetric group Sn conjugation by any odd permutation is an outer automorphism of An or more precisely "represents the class of the (non-trivial) outer automorphism of An", but the outer automorphism does not correspond to conjugation by any particular odd element, and all conjugations by odd elements are equivalent up to conjugation by an even element.However, for an abelian group A, the inner automorphism group is trivial and thus the automorphism group and outer automorphism group are naturally identified, and outer automorphisms do act on A.".
- Outer_automorphism_group wikiPageExternalLink v3.
- Outer_automorphism_group wikiPageID "628466".
- Outer_automorphism_group wikiPageLength "10000".
- Outer_automorphism_group wikiPageOutDegree "69".
- Outer_automorphism_group wikiPageRevisionID "646561263".
- Outer_automorphism_group wikiPageWikiLink Algebraically_closed_field.
- Outer_automorphism_group wikiPageWikiLink Alternating_group.
- Outer_automorphism_group wikiPageWikiLink Automorphism.
- Outer_automorphism_group wikiPageWikiLink Automorphism_group.
- Outer_automorphism_group wikiPageWikiLink Borel_subgroup.
- Outer_automorphism_group wikiPageWikiLink Category:Group_automorphisms.
- Outer_automorphism_group wikiPageWikiLink Category:Group_theory.
- Outer_automorphism_group wikiPageWikiLink Character_table.
- Outer_automorphism_group wikiPageWikiLink Classification_of_finite_simple_groups.
- Outer_automorphism_group wikiPageWikiLink Cokernel.
- Outer_automorphism_group wikiPageWikiLink Complete_group.
- Outer_automorphism_group wikiPageWikiLink Conjugacy_class.
- Outer_automorphism_group wikiPageWikiLink Conway_group.
- Outer_automorphism_group wikiPageWikiLink Cyclic_group.
- Outer_automorphism_group wikiPageWikiLink Dehn–Nielsen_theorem.
- Outer_automorphism_group wikiPageWikiLink Dihedral_group_of_order_6.
- Outer_automorphism_group wikiPageWikiLink Duality_(mathematics).
- Outer_automorphism_group wikiPageWikiLink Eulers_totient_function.
- Outer_automorphism_group wikiPageWikiLink Exact_sequence.
- Outer_automorphism_group wikiPageWikiLink Fundamental_group.
- Outer_automorphism_group wikiPageWikiLink General_linear_group.
- Outer_automorphism_group wikiPageWikiLink Geometric_group_action.
- Outer_automorphism_group wikiPageWikiLink Group_(mathematics).
- Outer_automorphism_group wikiPageWikiLink Group_of_Lie_type.
- Outer_automorphism_group wikiPageWikiLink Inner_automorphism.
- Outer_automorphism_group wikiPageWikiLink Integer.
- Outer_automorphism_group wikiPageWikiLink Kernel_(algebra).
- Outer_automorphism_group wikiPageWikiLink List_of_finite_simple_groups.
- Outer_automorphism_group wikiPageWikiLink Mapping_class_group.
- Outer_automorphism_group wikiPageWikiLink Mathematics.
- Outer_automorphism_group wikiPageWikiLink Mathieu_group.
- Outer_automorphism_group wikiPageWikiLink Multiplicative_group_of_integers_modulo_n.
- Outer_automorphism_group wikiPageWikiLink Odd_permutation.
- Outer_automorphism_group wikiPageWikiLink Out(Fn).
- Outer_automorphism_group wikiPageWikiLink Parity_of_a_permutation.
- Outer_automorphism_group wikiPageWikiLink Projective_linear_group.
- Outer_automorphism_group wikiPageWikiLink Projective_special_linear_group.
- Outer_automorphism_group wikiPageWikiLink Pun.
- Outer_automorphism_group wikiPageWikiLink Quotient_group.
- Outer_automorphism_group wikiPageWikiLink Reductive_group.
- Outer_automorphism_group wikiPageWikiLink Root_system.
- Outer_automorphism_group wikiPageWikiLink SO(8).
- Outer_automorphism_group wikiPageWikiLink Schreier_conjecture.
- Outer_automorphism_group wikiPageWikiLink Semidirect_product.
- Outer_automorphism_group wikiPageWikiLink Short_exact_sequence.
- Outer_automorphism_group wikiPageWikiLink Simple_group.
- Outer_automorphism_group wikiPageWikiLink Solvable_group.
- Outer_automorphism_group wikiPageWikiLink Spin(8).
- Outer_automorphism_group wikiPageWikiLink Surface.
- Outer_automorphism_group wikiPageWikiLink Symmetric_group.
- Outer_automorphism_group wikiPageWikiLink Topology.
- Outer_automorphism_group wikiPageWikiLink Triality.
- Outer_automorphism_group wikiPageWikiLink Trivial_group.
- Outer_automorphism_group wikiPageWikiLink File:Dynkin_diagram_D4.png.
- Outer_automorphism_group wikiPageWikiLinkText "''n'' = 6".
- Outer_automorphism_group wikiPageWikiLinkText "Outer automorphism group".
- Outer_automorphism_group wikiPageWikiLinkText "outer automorphism group".
- Outer_automorphism_group wikiPageWikiLinkText "outer automorphism".
- Outer_automorphism_group wikiPageWikiLinkText "outer automorphisms".
- Outer_automorphism_group hasPhotoCollection Outer_automorphism_group.
- Outer_automorphism_group wikiPageUsesTemplate Template:Citation_needed.
- Outer_automorphism_group wikiPageUsesTemplate Template:Details.
- Outer_automorphism_group wikiPageUsesTemplate Template:Refbegin.
- Outer_automorphism_group wikiPageUsesTemplate Template:Refend.
- Outer_automorphism_group wikiPageUsesTemplate Template:Refimprove.
- Outer_automorphism_group wikiPageUsesTemplate Template:Reflist.
- Outer_automorphism_group subject Category:Group_automorphisms.
- Outer_automorphism_group subject Category:Group_theory.
- Outer_automorphism_group hypernym Group.
- Outer_automorphism_group type Article.
- Outer_automorphism_group type Band.
- Outer_automorphism_group type Article.
- Outer_automorphism_group type Function.
- Outer_automorphism_group comment "In mathematics, the outer automorphism group of a group Gis the quotient Aut(G) / Inn(G), where Aut(G) is the automorphism group of G and Inn(G) is the subgroup consisting of inner automorphisms. The outer automorphism group is usually denoted Out(G). If Out(G) is trivial and G has a trivial center, then G is said to be complete.An automorphism of a group which is not inner is called an outer automorphism.".
- Outer_automorphism_group label "Outer automorphism group".
- Outer_automorphism_group sameAs Automorfismo_esterno.
- Outer_automorphism_group sameAs 외부자기동형군.
- Outer_automorphism_group sameAs Uitwendig_automorfisme.
- Outer_automorphism_group sameAs m.02ybff.
- Outer_automorphism_group sameAs Q3630548.
- Outer_automorphism_group sameAs Q3630548.
- Outer_automorphism_group sameAs 外自同構群.
- Outer_automorphism_group wasDerivedFrom Outer_automorphism_group?oldid=646561263.
- Outer_automorphism_group isPrimaryTopicOf Outer_automorphism_group.