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...

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...

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...

the case of groups that are noncommutative, a torsion element is an element of finite order. Contrary to the commutative case, the torsion elements do...

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

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...

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...

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...

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

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...

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...

Grigorchuk groups. International Journal of Algebra and Computation, vol. 11 (2001), no. 1, pp. 1–17. Laurent Bartholdi. The growth of Grigorchuk's torsion group...

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...

{\displaystyle A/S} , the group of n-torsion points forms a finite flat group scheme. The union of the p n {\displaystyle p^{n}} -torsion points, for all n,...

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

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...

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...

G} . If f {\displaystyle f} is a character of a finite group (or more generally a torsion group) G {\displaystyle G} , then each function value f ( g )...

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

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

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...

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

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...

infinite isometry groups; for example, the "cyclic group" (meaning that it is generated by one element – not to be confused with a torsion group) generated by...

subgroup of the multiplicative group of a field is necessarily cyclic. See Lang 2002, Theorem IV.1.9. The notions of torsion of a module and simple algebras...

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...

purely group-theoretic manner using the Lyndon–Hochschild–Serre spectral sequence. The cohomology groups Hn(G, M) of finite groups G are all torsion for...

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...

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...

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...