A torsion subgroup is a subset of a group that consists of all elements whose orders are finite. This means that for each element in the torsion subgroup, there exists a positive integer n such that the n-th power of the element is the identity element of the group. The torsion subgroup plays a crucial role in understanding the structure of abelian groups, especially in relation to the Structure Theorem for Finitely Generated Abelian Groups, as it helps identify how groups can be decomposed into simpler components.
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