Let G have order pq, where p and q are distinct primes. Prove G is either cyclic or every element x≠e in G has order p or q
Problem: Let have order , where are distinct primes. Prove is either cyclic or every element has order or
Proof: As was stated we know that if that . Now suppose that , we must have that and since are distinct primes this is only true if . If equals the first two we are done. Otherwise we'd have that which means that are distinct elements. If there existed a such that we'd have that which is clearly false. Thus .