Torsion abelian group

In abstract algebra, a torsion abelian group is an abelian group in which every element has finite order.Dummit, David; Foote, Richard. Abstract Algebra, , pp. 369 For example, the torsion subgroup of an abelian group is a torsion abelian group. Examples

Finite Cyclic

A finite cyclic group is a torsion abelian group.

Finitely Generated Abelian Group

A finitely generated abelian group is torsion iff it is finite, see Finitely generated abelian group#Classification

Infinite Torsion Abelian Group

A torsion abelian group is not necessarily finite. For instance, the group /

See also

Betti number

References