# regular covering transformation

can you help me with proving this statement?

> Suppose that $$F:S^1\longrightarrow S^1$$ such that $$F(z)=z^n$$ , is a covering space.prove that $$F$$ is regular covering transformation

Honestly..i don't have any ideal to prove this statement. Your help would be very useful for me

$$F$$ is a regular covering transformation if $$F_{*}(\pi_1(S^1, s_0)) \lhd \pi_1(S^1, s_0).$$ But $$\pi_1(S^1, s_0) \cong \mathbb{Z}$$ is abelian, so every subgroup is normal, and hence every covering map is regular.
$$F_{*}(\pi_1(S^1, S_0))$$ is a subgroup of $$\pi_1(S^1, s_0)$$ since the induced map of $$F$$, $$F_{*}$$, is a homomorphism.