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Algebra factor group, Is solution correct?

  1. Oct 6, 2014 #1
    1. The problem statement, all variables and given/known data
    G is a finite group. K is normal to G. If 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
    (Kg)^n = K for some Kg in G/K.

    (Kg)^n = (Kg^n) = K, hence g^n = 1 where g is an element of G.

    Is this all there was to it? Did I skip a step going from (Kg)^n --> (Kg^n)
  2. jcsd
  3. Oct 6, 2014 #2


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    Science Advisor
    Homework Helper

    Not correct. Very sloppy. Kg^n=K doesn't tell you g^n=1. It tells you g^n is an element of K.
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