1. The problem statement, all variables and given/known data Find all elements x in S4 such that x4 = e. (e is the identity) 2. Relevant equations Cycle notation is advised. 3. The attempt at a solution I know there are 4 elements in this (1 2 3 4). And I feel like I need to find the order of S which can be found by finding the number of cycles. Suppose S is a finite group with x elements, then xn = e for all x in S. That's my start. not sure where to go from there.