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identity element of group

См. также в других словарях:

  • Identity — may refer to:Philosophy* Identity (philosophy), the sameness of two things * Identity theory of mind, in the philosophy of mind, holds that the mind is identical to the brain * Personal identity (philosophy) * Identity (social science) * Identity …   Wikipedia

  • group — [gro͞op] n. [Fr groupe < It gruppo, a knot, lump, group < Gmc * kruppa, round mass: see CROP] 1. a number of persons or things gathered closely together and forming a recognizable unit; cluster; aggregation; band [a group of houses] 2. a… …   English World dictionary

  • 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

  • Group isomorphism — In abstract algebra, a group isomorphism is a function between two groups that sets up a one to one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two… …   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

  • Group object — In category theory, a branch of mathematics, group objects are certain generalizations of groups which are built on more complicated structures than sets. A typical example of a group object is a topological group, a group whose underlying set is …   Wikipedia

  • Group homomorphism — In mathematics, given two groups ( G , *) and ( H , ·), a group homomorphism from ( G , *) to ( H , ·) is a function h : G → H such that for all u and v in G it holds that: h(u*v) = h(u) h(v) where the group operation on the left hand side of the …   Wikipedia

  • group — groupwise, adv. /groohp/, n. 1. any collection or assemblage of persons or things; cluster; aggregation: a group of protesters; a remarkable group of paintings. 2. a number of persons or things ranged or considered together as being related in… …   Universalium

  • 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

  • Identity component — In mathematics, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group. Similarly, the identity path component of a topological group G is the path component of G that… …   Wikipedia

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