1. The problem statement, all variables and given/known data If G is a group with n elements and g ∈ G, show that g^n = e, where e is the identity element. 2. Relevant equations 3. The attempt at a solution I feel like there is missing information, but that cannot be. This seems too simple: The order of G is the smallest possible integer n such that g^n = e. If no such n exists, then G is of infinite order. From this definition of order can we simply state that since G is a group with 'n' elements then there must exist an n such that g^n = e ? order is denoted as °(g) So °(g) = n ==> g^n = e.