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* In abstract algebra, a group is torsion-free if the only element of finite order is the identity.
* In differential geometry, an
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Torsion-free 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
torsion-free group — /tawr sheuhn free /, Math. a group in which every element other than the identity has infinite order. * * * … Universalium
torsion-free group — /tawr sheuhn free /, Math. a group in which every element other than the identity has infinite order … Useful english dictionary
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
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 tensor — In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve. The torsion of a curve, as it appears in the Frenet Serret formulas, for instance, quantifies the twist of a curve… … 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
Torsion spring — A mousetrap powered by a helical torsion spring A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. The amount of force (actually torque) it exerts… … Wikipedia
torsion bar — A long spring steel rod attached in such a way that one end is anchored while the other is free to twist. One end is fastened to the frame at one end and to a suspension part at the other. If an arm is attached, at right angles, to the free end,… … Dictionary of automotive terms
Whitehead torsion — In mathematics, Whitehead torsion is an invariant of an h cobordism in a Whitehead group, that is important in simple homotopy theory and surgery theory. It is named for J. H. C. Whitehead.Whitehead torsionSuppose that W is an h cobordism from M… … Wikipedia
