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Modern Algebra Factor Groups question

  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    If K is normal in G and |g| = n for some g in G, show that the order of Kg in G/K divides n.

    2. Relevant equations
    None

    3. The attempt at a solution
    Okay so I feel like I have a solution but I don't use all the information given so I'm trying to find holes in it...

    g^n = 1

    K = Kg^n = (Kg)^n. So it seems If we take Kg to the nth power we get it's identity. This means that the order of Kg must divide n.

    What am I missing here?
     
  2. jcsd
  3. Oct 4, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you mean you aren't using that K is normal in G, you need that fact to justify saying (Kg)^n=Kg^n, or even that G/K is a group. Better review why.
     
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