irreducible group

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• Irreducible — may be used to refer to many different things.* In mathematics, the term irreducible is used in many different, unrelated fields; its use often follows from the denotative meaning of the word irreducible . *irreducible (philosophy) * Irreducible… …   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

• Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

• Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   Wikipedia

• Group algebra — This page discusses topological algebras associated to topological groups; for the purely algebraic case of discrete groups see group ring. In mathematics, the group algebra is any of various constructions to assign to a locally compact group an… …   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 ring — This page discusses the algebraic group ring of a discrete group; for the case of a topological group see group algebra, and for a general group see Group Hopf algebra. In algebra, a group ring is a free module and at the same time a ring,… …   Wikipedia

• irreducible — irreducibility, irreducibleness, n. irreducibly, adv. /ir i dooh seuh beuhl, dyooh /, adj. 1. not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum. 2. incapable of being brought into a… …   Universalium

• Lorentz group — Group theory Group theory …   Wikipedia

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

• Complex reflection group — In mathematics, a complex reflection group is a group acting on a finite dimensional complex vector space, that is generated by complex reflections: non trivial elements that fix a complex hyperplane in space pointwise. (Complex reflections are… …   Wikipedia