**Fundamental group** — In mathematics, the fundamental group is one of the basic concepts of algebraic topology. Associated with every point of a topological space there is a fundamental group that conveys information about the 1 dimensional structure of the portion of … Wikipedia

**fundamental group** — noun : a set that is a subset of all paths defined on a set of points each pair of which is joined by a path and that is the quotient group of the group of all paths beginning and ending in the given point … Useful english dictionary

**fundamental group** — noun The group whose elements are homotopy classes of images of the closed interval in a specified topological space, such that the endpoints are both mapped to a designated point, and whose operation is concat … Wiktionary

**Induced homomorphism (fundamental group)** — In mathematics, especially in the area of topology known as algebraic topology, the induced homomorphism is a group homomorphism related to the study of the fundamental group.DefinitionLet X and Y be topological spaces; let x 0 be a point of X… … Wikipedia

**Étale fundamental group** — The étale fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.Topological analogueIn algebraic topology, the fundamental group :pi 1(T) of a connected topological space T is… … 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

**Fundamental polygon** — In mathematics, each closed surface in the sense of geometric topology can be constructed from an even sided oriented polygon, called a fundamental polygon, by pairwise identification of its edges. Fundamental parallelogram defined by a pair of… … 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 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 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