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Sylow Question

  1. Feb 24, 2005 #1
    Hello!

    For the life of me, I can't seem to figure this out (vapor lock in the ol' brain):

    Show that if G has only 1 p-Sylow subgroup, then it must be normal.

    I know it something to do with showing it's a conjugate to itself (right coset = left coset?). I'm just not quite sure how to go about showing this.

    Thanks for your time, help, and patience with me.

    dogma
     
  2. jcsd
  3. Feb 24, 2005 #2

    matt grime

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    Let S be the sylow subgroup. gSg^{-1} is another sylow subgroup, and must be S as S is unique.
     
  4. Feb 24, 2005 #3
    thanks

    Thank you....that makes sense.

    dogma
     
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