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.

  • $\begingroup$ Thank you a lot this is the right answer i wanted...Can you help me for the solution of my one question before the end that i asked before this question? @klint $\endgroup$ – pershina olad Jan 8 at 21:22

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