Group theory, is my solution correct?

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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:H] = 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!
 

Answers and Replies

  • #2
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This is a correct proof.
 

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