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Proving H is normal

  1. Oct 31, 2008 #1
    I have been struggling with this proof:

    If G is a finite group with exactly one subgroup H of a given order, then H is normal.

    I'm not sure where to start...
     
  2. jcsd
  3. Oct 31, 2008 #2

    Office_Shredder

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    What can you say about xHx-1 for any x in G?

    You only need to write down the definitions and it becomes obvious
     
  4. Oct 31, 2008 #3
    What can you say about the left and right cosets of H in G? Do they coincide under those conditions?

    Once you can establish that, it is trivial.
     
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