G is a finite group. K is normal to G. If G/K has an element of order n, show that G has an element of order n.
The Attempt at a Solution
(Kg)^n = K for some Kg in G/K.
(Kg)^n = (Kg^n) = K, hence g^n = 1 where g is an element of G.
Is this all there was to it? Did I skip a step going from (Kg)^n --> (Kg^n)