permutation group
noun Date: 1904 a group whose elements are permutations and in which the product of two permutations is a permutation whose effect is the same as the successive application of the first two

New Collegiate Dictionary. 2001.

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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… …   Wikipedia

  • permutation group — kėlinių grupė statusas T sritis fizika atitikmenys: angl. permutation group vok. Permutationsgruppe, f rus. группа перестановок, f pranc. groupe de permutations, m …   Fizikos terminų žodynas

  • permutation group — noun : a group of which the elements are permutations and in which the product of two permutations is a permutation whose effect is the same as the successive application of the first two * * * a mathematical group whose elements are permutations …   Useful english dictionary

  • permutation group — a mathematical group whose elements are permutations and in which the product of two permutations is the same permutation as is obtained by performing them in succession. [1900 05] * * * …   Universalium

  • Primitive permutation group — In mathematics, a permutation group G acting on a set X is called primitive if G preserves no nontrivial partition of X . In the other case, G is imprimitive. An imprimitive permutation group is an example of an induced representation; examples… …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Permutation — For other uses, see Permutation (disambiguation). The 6 permutations of 3 balls In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values.… …   Wikipedia

  • Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   Wikipedia

  • permutation — [pʉr΄myo͞o tā′shən] n. [ME permutacion < MFr < L permutatio < permutare: see PERMUTE] 1. any radical alteration; total transformation 2. a) a complete rearrangement, esp. by interchanging b) Math. any of the total number of groupings, or …   English World dictionary

  • Permutation matrix — In mathematics, in matrix theory, a permutation matrix is a square (0,1) matrix that has exactly one entry 1 in each row and each column and 0 s elsewhere. Each such matrix represents a specific permutation of m elements and, when used to… …   Wikipedia

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