Torsion abelian group information

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...

of 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...

mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does...

torsion abelian group is an abelian group in which every element has finite order. A torsion-free abelian group is an abelian group in which the identity element...

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...

Hamiltonian group is a direct product of the form G = Q8 × B × D, where B is an elementary abelian 2-group, and D is a torsion abelian group with all elements...

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...

algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by...

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...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

that A(K), the group of points on A over K, is a finitely-generated abelian group. A great deal of information about its possible torsion subgroups is known...

In mathematics, specifically in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided...

group is a torsion-free abelian group that is "small" in a sense that is made precise in the definition below. Let ZN denote the Baer–Specker group,...

divisible abelian group whose torsion subgroup is the same as the torsion subgroup of T {\displaystyle \mathbb {T} } . Mathematics portal Group of rational...

generated abelian groups as the torsion groups that cannot be expressed as a direct sum of two non-trivial groups. As such they, along with the group of integers...

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...

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...

nilpotent group is a group that is "almost abelian". This idea is motivated by the fact that nilpotent groups are solvable, and for finite nilpotent groups, two...

For example, the p-torsion of an elliptic curve in characteristic zero is locally isomorphic to the constant elementary abelian group scheme of order p2...

any abelian group, to deduce that the only simple abelian groups are the cyclic groups of prime order. The classification of nonabelian simple groups is...

be an abelian group in which every element has finite order (that is G is a torsion abelian group; for example G can be a finite abelian group or Q /...

G-group; in effect, a generalization of a module to non-Abelian coefficients. These algebraic ideas are closely related to topological ideas. The group...

M. C. R. Butler (1965). Butler, M. C. R. (1965), "A class of torsion-free abelian groups of finite rank", Proc. London Math. Soc., Series 3, 15: 680–698...

torsion-free abelian group is bi-orderable; this is still true for nilpotent groups but there exist torsion-free, finitely presented groups which are not...