Let $a$ be an element of $S_n$ ,the permutation group of order n. $a^k$ is a cycle of length n. Then what is the order of $a$?
If $n$ is prime then a should be a cycle of length $n$.But if $n$ is not prime then how to find the order of $a$? Let $a$ can be expressed as the product of some disjoint cycles. Then the order of $a$ is lcm of the length of the disjoint cycles and $n$ should divide the order of $a$. After that, I'm not getting anything.