Torsion group

Torsion subgroup of an abelian group

Given an Abelian group we may form the torsion subgroup containing all elements of finite order, i.e. . #m/def/group #m/thm/group

Proof of subgroup

Clearly , so the set is inhabited. Let , so that there exist such that . Then , hence . Therefore is a subgroup by One step subgroup test.

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