# Show the range of f is isomorphic to a quotient of z

## Homework Statement

Let G be any group and a in G, define f: Z → G by f(n) = a^n

Apply any isomorphism theorem to show that range of f is isomorphic to a quotient group of Z

## The Attempt at a Solution

The range of f is a^n , then quotient group of Z is Z/nZ
Apply the first isomorphism theorem , we have a^n isomorphic with Z/nZ