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full commutator group

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  • 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

  • Rotation group — This article is about rotations in three dimensional Euclidean space. For rotations in four dimensional Euclidean space, see SO(4). For rotations in higher dimensions, see orthogonal group. In mechanics and geometry, the rotation group is the… …   Wikipedia

  • Binary icosahedral group — In mathematics, the binary icosahedral group is an extension of the icosahedral group I of order 60 by a cyclic group of order 2. It can be defined as the preimage of the icosahedral group under the 2:1 covering homomorphism:mathrm{Sp}(1) o… …   Wikipedia

  • Quaternion group — In group theory, the quaternion group is a non abelian group of order 8. It is often denoted by Q and written in multiplicative form, with the following 8 elements : Q = {1, −1, i , − i , j , − j , k , − k }Here 1 is the identity element, (−1)2 …   Wikipedia

  • Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry …   Wikipedia

  • Free group — In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st 1 =… …   Wikipedia

  • History of group theory — The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry.… …   Wikipedia

  • Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… …   Wikipedia

  • Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… …   Wikipedia

  • Bracket — 〈 redirects here. It is not to be confused with く, a Japanese kana. This article is about bracketing punctuation marks. For other uses, see Bracket (disambiguation). Due to technical restrictions, titles like :) redirect here. For typographical… …   Wikipedia

  • Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

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