1. The problem statement, all variables and given/known data Let G be a finite group and let K be normal to G. If the factor group G/K has an element of order n, show that G has an element of order n. 2. Relevant equations None 3. The attempt at a solution Lets say Kg is the element in G/K with order n. That means: (Kg)^n = K and from properties of factor groups we know: (Kg)^n = Kg^n so Kg^n = K hence g^n = 1 if g^n = 1 then it must be in G, because G has the identity (1). Is this correct thinking?