symmetric group
noun Date: 1897 a permutation group that is composed of all of the permutations of n things

New Collegiate Dictionary. 2001.

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• Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …   Wikipedia

• symmetric group — noun : a permutation group that is composed of all of the permutations of n things * * * Math. the group of all permutations of a finite set. Cf. alternating group. [1905 10] …   Useful english dictionary

• symmetric group — Math. the group of all permutations of a finite set. Cf. alternating group. [1905 10] * * * …   Universalium

• symmetric group — noun A group whose elements are precisely all of the bijections of some set with itself and whose operation is composition of those bijections …   Wiktionary

• Representation theory of the symmetric group — In mathematics, the representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be obtained. This has a large area of potential applications, from… …   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

• Symmetric algebra — In mathematics, the symmetric algebra S ( V ) (also denoted Sym ( V )) on a vector space V over a field K is the free commutative unital associative K algebra containing V .It corresponds to polynomials with indeterminates in V , without choosing …   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

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Symmetric product of an algebraic curve — In mathematics, the n fold symmetric product of an algebraic curve C is the quotient space of the n fold cartesian product: C times; C times; ... times; C or C n by the group action of the symmetric group on n letters permuting the factors. It… …   Wikipedia