 torsionfree group

/tawr"sheuhn free'/, Math.a group in which every element other than the identity has infinite order.
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Universalium. 2010.
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Universalium. 2010.
torsionfree group — /tawr sheuhn free /, Math. a group in which every element other than the identity has infinite order … Useful english dictionary
Torsionfree abelian groups of rank 1 — Infinitely generated abelian groups have very complex structure and are far less well understood than finitely generated abelian groups. Even torsion free abelian groups are vastly more varied in their characteristics than vector spaces. Torsion… … Wikipedia
Torsionfree — In mathematics, the term torsion free may refer to several unrelated notions: * In abstract algebra, a group is torsion free if the only element of finite order is the identity. * In differential geometry, an affine connection is torsion free if… … 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
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 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
Torsion subgroup — In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order. An abelian group A is called a torsion (or periodic) group if every element of A has finite… … Wikipedia
Torsion (algebra) — In abstract algebra, the term torsion refers to a number of concepts related to elements of finite order in groups and to the failure of modules to be free. Definition Let G be a group. An element g of G is called a torsion element if g has… … 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 (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