1. The problem statement, all variables and given/known data If G is a finite group such that all elements have prime order(other than the identity). If G has a non-trivial center then show every element has the same order. 2. Relevant equations 3. The attempt at a solution Since we know that G has a center, we know that there is atleast one element that commutes with every element in G. I'm not sure how we can show that all elements have the same order from just this.