roblem 7. Let G be an Abelian group. The torsion subgroup T of G is the set T = {g €G: ord(g) is finite} Show that T is a subgroup of G. (Problem 3a) should be helpful in this part.) Show that T is a normal subgroup of G. (Problem 3b) should be helpful in this part.) Show that the factor group G/T is torsion-free, that is, the only element of G/T which has finite order is the identity element.

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