The torsion subgroup of an abelian group consists of all elements of finite order. For a finitely generated abelian group, it is the finite direct summand complementary to the free abelian part.
In the context of group theory, particularly in the study of abelian groups (and more generally, in the context of modules over a ring), the **torsion subgroup** is an important concept. The torsion subgroup of an abelian group \( G \) is defined as the set of elements in \( G \) that have finite order.
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