Proving 1 p-Sylow Subgroup of G is Normal

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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
 
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Let S be the sylow subgroup. gSg^{-1} is another sylow subgroup, and must be S as S is unique.
 
thanks

Thank you...that makes sense.

dogma
 

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