Question: Let G be an abelian group and use additive notation. Call G a divisible group if given x e G and a positive integer m

Let G be an abelian group and use additive notation. Call G a divisible group if given x e G and a positive integer m we can always find an element y of G such that my = x. For example, Q, R, C, and C are all divisible groups. Show that Z and QP" are not divisible. Prove that a non-trivial divisible group cannot be finitely generated.

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