Algebra factor group, Is solution correct?

[PsychonautQQ]

Homework Statement

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.

Homework Equations

none.

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)

 

[Dick]

Not correct. Very sloppy. Kg^n=K doesn't tell you g^n=1. It tells you g^n is an element of K.