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Normal Subgroups

  1. Jul 27, 2010 #1
    1. The problem statement, all variables and given/known data


    If N is a normal subgroup in the finite group such that number of cosets of N in G [G:N] and o(N) are relatively prime, then show that any element x in G satisfying x^o(N) = e must be in N?


    2. Relevant equations



    3. The attempt at a solution

    For any x in G, Nx will be an element in G/N . As N is normal, G/N is a group.
    By Lagrangian Theorem, we will have x^o(G/N) belongs to N.
    I am not able to get any clue after making lot of attempts beyond this point.

    Can you please throw some light regarding this?

    Regards,
    Henry.
     
    Last edited: Jul 27, 2010
  2. jcsd
  3. Jul 27, 2010 #2

    Office_Shredder

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    Consider the coset xN
     
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