Let G be an abelian group and let z, y E G. Suppose that z and...

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Let G be an abelian group and let z, y E G. Suppose that z and y are both of finite order. Show that ay is of finite order and that o(zy) divides o(x)o(y). Let G be an abelian group and let z, y E G. Suppose that z and y are both of finite order. Show that ay is of finite order and that o(zy) divides o(x)o(y).

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Proof Since G is ab el ian we have r y yr Now since x and y are both of fini... View the full answer