In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which every element has finite order. The exponent of such...

elements of the group.: 49–50  Finite abelian groups and torsion groups have rank zero, and every abelian group of rank zero is a torsion group. The integers...

abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order (the torsion elements...

theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian...

ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of...

up torsion in Wiktionary, the free dictionary. Torsion may refer to: Torsion (mechanics), the twisting of an object due to an applied torque Torsion of...

algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is...

torsion abelian group is an abelian group in which every element has finite order. For example, the torsion subgroup of an abelian group is a torsion...

the group of permutations of an infinite set), or which exhibit some pathological behavior (for example, finitely generated infinite torsion groups). A...

abelian group: every finite abelian group is a direct sum of primary cyclic groups. Denote the torsion subgroup of G as tG. Then, G/tG is a torsion-free...

In mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank...

E(K)_{\text{tors}},} where E ( K ) tors {\displaystyle E(K)_{\text{tors}}} is the torsion group of E, for which comparatively much is known, and r ∈ Z ≥ 0 {\displaystyle...

In abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion-free group splits. If the group is M {\displaystyle...

/ S, the group of n-torsion points forms a finite flat group scheme. The union of the pn-torsion points, for all n, forms a p-divisible group. Deformations...

domain where zero is the only torsion element Torsion-free abelian group, an abelian group which is a torsion-free group Torsion-free rank, the cardinality...

up torsion in Wiktionary, the free dictionary. Torsion is a gastropod synapomorphy which occurs in all gastropods during larval development. Torsion is...

faster than the speed of light. The first torsion field proposals were proposed in the late Soviet Union by a group of physicists in the 1980s who loosely...

group operation given by the tensor product of algebras. The resulting group is called the Brauer group Br(F) of the field F. It is always a torsion group...

if and only if it has no local torsion sections. Torsion (algebra) torsion-free abelian group torsion-free abelian group of rank 1; the classification...

devised sometime before 1783 by geologist John Michell, who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing...

In mathematics, a torsion sheaf is a sheaf of abelian groups F {\displaystyle {\mathcal {F}}} on a site for which, for every object U, the space of sections...

they force the group orders of the curve modulo primes to be divisible by 12 and 16 respectively. The following curves have a torsion group isomorphic to...

In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister...

known that the Tate–Shafarevich group is a torsion group, thus the conjecture is equivalent to stating that the group is finitely generated. The Cassels–Tate...

an invariant called the torsion. The torsion of a homotopy equivalence takes values in a group now called the Whitehead group and denoted Wh(π), where...

homotopy equivalence is its Whitehead torsion τ ( f ) {\displaystyle \tau (f)} which is an element in the Whitehead group Wh ⁡ ( π 1 ( Y ) ) {\displaystyle...

M(n2, K), where n is the degree of A over K. The Brauer group of any field is a torsion group. In more detail, define the period of a central simple algebra...

non-torsion coefficients. To get cohomology groups without torsion from étale cohomology one has to take an inverse limit of étale cohomology groups with...

torsion-free abelian groups are free abelian. The additive group of rational numbers Q {\displaystyle \mathbb {Q} } provides an example of a torsion-free...

the order of the torsion group, # S h a ( E ) = {\displaystyle \#\mathrm {Sha} (E)=} #Ш(E) is the order of the Tate–Shafarevich group, Ω E {\displaystyle...