trivial group

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• Trivial group — In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group, variously labeled e , 1, or 0, is the identity element.… …   Wikipedia

• Trivial (mathematics) — In mathematics, the term trivial is frequently used for objects (for examples, groups or topological spaces) that have a very simple structure. For non mathematicians, they are sometimes more difficult to visualize or understand than other, more… …   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 (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 cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   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 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

• Trivial representation — In the mathematical field of representation theory, a trivial representation is a representation ( V , phi; ) of a group G on which all elements of G act as the identity mapping of V . A trivial representation of an associative or Lie algebra is… …   Wikipedia

• Trivial Pursuit — For other uses, see Trivial Pursuit (disambiguation). Trivial Pursuit Players 2 6 (teams allowed) Age range 15+ Setup time 5 minutes Playing time 30 minutes (varies widely) …   Wikipedia

• Cyclic group — Group theory Group theory …   Wikipedia