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...
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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...
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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...
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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...
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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...
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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...
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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...
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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...
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the group of permutations of an infinite set), or which exhibit some pathological behavior (for example, finitely generated infinite torsion groups). A...
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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...
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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...
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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...
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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...
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Abelian variety (redirect from Semiabelian group scheme)
/ 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...
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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...
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up torsion in Wiktionary, the free dictionary. Torsion is a gastropod synapomorphy which occurs in all gastropods during larval development. Torsion is...
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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...
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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...
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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...
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Cavendish experiment (redirect from Torsion bar experiment)
devised sometime before 1783 by geologist John Michell, who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing...
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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...
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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...
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In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister...
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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...
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Algebraic K-theory (redirect from Algebraic K-group)
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...
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homotopy equivalence is its Whitehead torsion τ ( f ) {\displaystyle \tau (f)} which is an element in the Whitehead group Wh ( π 1 ( Y ) ) {\displaystyle...
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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...
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Étale cohomology (section ℓ-adic cohomology groups)
non-torsion coefficients. To get cohomology groups without torsion from étale cohomology one has to take an inverse limit of étale cohomology groups with...
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torsion-free abelian groups are free abelian. The additive group of rational numbers Q {\displaystyle \mathbb {Q} } provides an example of a torsion-free...
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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...
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