Homomorphism theorem/Application to 1 to g/Exercise

Let ${}G$ be a group, and ${}g\in G$ be an element, together with the (according to fact) corresponding group homomorphism

$\varphi \colon \mathbb {Z} \longrightarrow G,n\longmapsto g^{n}.$

Describe the canonical factorization of ${}\varphi$ in the sense of fact.

Create a solution