Torsion (abstract algebra)
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In mathematics, torsion (from latin torquere: to turn, to twist), is a concept in abstract algebra.
The torsion subgroup of an abelian group consists of all elements of finite order. An abelian group is called torsion-free if and only if the identity is the only element that has finite order. (This concept generalises to that of a torsion module.) In the Tor functors of homological algebra, which arise because tensor product does not in general preserve exact sequences, the symbol Tor does stand for this kind of algebraic torsion, historically speaking anyway. These functors were introduced in order to make systematic the universal coefficient theorem of homology theory, in cases where the homology groups Hi(X, Z) of a space X had some torsion.
[edit] Topology
Some topological invariants are called torsions: for example the Reidemeister-Schreier torsion of a group acting on a finite complex; and also the analytic torsion defined using Laplacians.
