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Permutation group

In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation…

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Overview

Basic properties and terminology

Notation

Composition of permutations–the group product

Neutral element and inverses

Examples

Group actions

Transitive actions

Cayley's theorem

Isomorphisms of permutation groups

Oligomorphic groups

History

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Permutation group

Nodes66
Edges65
Triples96
Avg. degree1.97
Density0.030303
Components1

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Permutation group

Top relations

related to References · 23
Permutation group → Abstract Algebra, Algebra, Algorithms, Applications, Artin, Brian, Cambridge University Press, Combinatorics, First Course, Graduate Texts, ISBN, John, Joseph, Mathematics, Michael, Mortimer, Pearson Prentice-Hall, Permutation Groups, Peter, Prentice-Hall
related to Further reading · 21
Permutation group → Akos Seress, Cambridge, Cambridge Tracts, Cambridge University Press, Cameron, Dugald Macpherson, Infinite Permutation Groups, Lecture Notes, LMS Student Text, Mathematics, Meenaxi Bhattacharjee, Möller, Neumann, Notes, Number, Oligomorphic Permutation Groups, Permutation, Permutation Groups, Peter, Rögnvaldur
related to history · 13
Permutation group → Algébriques, Camille Jordan, Cayley, Cayley's, Galois, Jordan's, Lagrange, Permutations, Substitutions, The, This, Traité, When Cayley
related to Cayley's theorem · 9
Permutation group → Any, Cayley's, Each, For, G1, In, Let, That, The
related to Composition of permutations–the group product · 9
Permutation group → For, However, In, Note, Since, Some, The, This, With
related to External links · 9
Permutation group → Alexander Hulpke, Archived, EMS Press, Encyclopedia, GAP Data Library, Mathematics, Permutation, Transitive Permutation Groups, Wayback Machine
related to Basic properties and terminology · 4
Permutation group → By Lagrange's, It, Sn, The
related to Isomorphisms of permutation groups · 3
Permutation group → If, Sym, The
related to Primitive actions · 3
Permutation group → For, On, Otherwise
is a · 2
Permutation group → group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G, subgroup of a symmetric group

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Important terminology

group permutation set permutations groups elements action composition given element product two identity first symmetric order square written notation example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Permutation groupis agroup G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G0.90text
Permutation groupis asubgroup of a symmetric group0.90text
Permutation grouprelated to Basic properties and terminologyIt0.60section
Permutation grouprelated to Basic properties and terminologyThe0.60section
Permutation grouprelated to Basic properties and terminologyBy Lagrange's0.60section
Permutation grouprelated to Basic properties and terminologySn0.60section
Permutation grouprelated to Cayley's theoremAny0.60section
Permutation grouprelated to Cayley's theoremIn0.60section
Permutation grouprelated to Cayley's theoremThat0.60section
Permutation grouprelated to Cayley's theoremFor0.60section
Permutation grouprelated to Cayley's theoremEach0.60section
Permutation grouprelated to Cayley's theoremCayley's0.60section

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