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.