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Working with Factor Groups

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Let G be a finite group and let K be normal to G. If the factor group G/K has an element of order n, show that G has an element of order n.

    2. Relevant equations

    3. The attempt at a solution
    Lets say Kg is the element in G/K with order n.
    That means:
    (Kg)^n = K

    and from properties of factor groups we know:
    (Kg)^n = Kg^n
    so Kg^n = K
    hence g^n = 1
    if g^n = 1 then it must be in G, because G has the identity (1).

    Is this correct thinking?
  2. jcsd
  3. Oct 26, 2014 #2


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    Science Advisor
    Homework Helper

    No. Haven't you posted this before? Kg^n=K only tells you that g^n is in K.
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