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The Homomorphism Theorems

  1. Oct 15, 2007 #1
    1. The problem statement, all variables and given/known data
    If G is a group and N is a normal subgroup of G, show that if a in G has finite order o(a), then Na in G/N has finite order m, where m divides o(a).


    2. Relevant equations



    3. The attempt at a solution
    I have no idea where to start. The problem says to prove it by using the homomorphism of G onto G/N.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2007 #2
    Try taking a look at using Lagrange's Theorem.
     
  4. Oct 22, 2009 #3
    I don't mean to dig this up, but isn't there a theorem (not sure if it lagrange) that states that the minimum order of an element to belong in a subgroup is a divisor of the group order. Couldn't one arrive at this by creating a bijection and then invoking the fact that |G:N|=|G|/|N|. <= That was something given to us in class that led to Lagrange's theorem.
     
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