1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook