Group/Element order/Z mod d/Exercise

Let ${}G$ be a group, and let ${}g\in G$ an element of finite order. Show that the order of ${}g$ coincides with the minimal ${}d\in \mathbb {N} _{+}$ such that there exists a group homomorphism

$\mathbb {Z} /(d)\longrightarrow G$

with the property that ${}g$ belongs to the image.

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