Torsion abelian group

In abstract algebra, a 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 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

Infinite Torsion Abelian Group

A torsion abelian group is not necessarily finite. For instance, the group $\mathbb{\mathbb{Q}}$/ $\mathbb{\mathbb{Z}}$

See also

• Betti number