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Group theory, is my solution correct?

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data

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

    3. 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!
  2. jcsd
  3. Apr 7, 2010 #2
    This is a correct proof.
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