Is $A_n$ isomorphic to $C_n$ in general Let $A_n$ denote the alternating group of order $n$, and let $C_n$ be the cyclic group of order $n$. Correct me if I'm wrong, but I know that $A_3 = \{(),(1,2,3),(1,3,2)\}\cong \{0,1,2\}=C_3$. I'm not really sure why, but I'm just accepting it. Is it true in general that $A_n\cong C_n$ for all $n\in\mathbb{N}_{>0}$

No, It is not.
$A_4$ has $12$ elements so It can not ismomorphic to $C_4$ !. But Actually, $A_n$ is not even abelian for $n\geq 4$.
