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...

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...

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...

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...

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...

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...

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 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...

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...

{\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,...

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...

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...

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

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...

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

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...

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

between the first Tor group Tor1 and the torsion subgroup of an abelian group. In the special case of abelian groups, Tor was introduced by Eduard Čech (1935)...

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...

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...

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...

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...

groups. Similarly algebraic K-theory relies in a way on classifying spaces of groups. Finally, the name of the torsion subgroup of an infinite group shows...

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 )...

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

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...