Locally cyclic group — In group theory, a locally cyclic group is a group ( G , *) in which every finitely generated subgroup is cyclic.ome facts*Every cyclic group is locally cyclic, and every locally cyclic group is abelian. *Every finitely generated locally cyclic… … 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
Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… … Wikipedia
Free abelian group — In abstract algebra, a free abelian group is an abelian group that has a basis in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients … Wikipedia
Free product — In abstract algebra, the free product of groups constructs a group from two or more given ones. Given, for example, groups G and H , the free product G*H can be constructed as follows: given presentations of G and of H , take the generators of G… … 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 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
Cyclic vomiting syndrome — Classification and external resources ICD 9 536.2 OMIM 500007 DiseasesDB … Wikipedia
Orthogonal group — Group theory Group theory … Wikipedia
Cyclic number (group theory) — A cyclic number[1] is a natural number n such that n and φ(n) are coprime. Here φ is Euler s totient function. An equivalent definition is that a number n is cyclic iff any group of order n is cyclic. Any prime number is clearly cyclic. All… … Wikipedia
