1. The problem statement, all variables and given/known data If G is a group of even order, show that it has an element g not equal to the identity such that g^2 = 1. 2. Relevant equations None 3. The attempt at a solution What I wrote: If |G| = n, then g^n = 1 for some g in G. Thus, (g^(n/2))(g^(n/2)) = 1, so g^(n/2) is the element of order 2. Is this a flawed argument? there guaranteed to be an element such that g^n = 1?