Algebra factor group, Is solution correct?

  • #1
784
11

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)
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
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Not correct. Very sloppy. Kg^n=K doesn't tell you g^n=1. It tells you g^n is an element of K.
 

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