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homomorphism 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

  • 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 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 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 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

  • 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

  • homomorphism — homomorphous, adj. /hoh meuh mawr fiz euhm, hom euh /, n. 1. Biol. correspondence in form or external appearance but not in type of structure or origin. 2. Bot. possession of perfect flowers of only one kind. 3. Zool. resemblance between the… …   Universalium

  • Homomorphism — In abstract algebra, a homomorphism is a structure preserving map between two algebraic structures (such as groups, rings, or vector spaces). The word homomorphism comes from the Greek language: ὁμός (homos) meaning same and μορφή (morphe)… …   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 extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… …   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

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