Group theory, is my solution correct?

[a1010711]

Homework Statement

if H is a normal subgroup of G and has index n, show that g^n is in H for all g in G.

The Attempt at a Solution

Take H a normal subgroup of a group G. Take g in G.

Consider gH in the quotient group G/H. Because |G/H| = [G] = n, (gH)^n = eH.

But g^nH = (gH)^n = eH. Thus g^n is in H.


please tell me if this is right or what i need to add,, thanks for your help!

 

[ystael]

This is a correct proof.