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I First Sylow Theorem

  1. Nov 17, 2016 #1
    Hello! I am a bit confused about the first Sylow theorem. So it says that if you have a group of order ##p^mn##, with gcd(n,p)=1, you must have a subgroup H of G of order ##p^m##. So, if I have a group G of order ##p^k##, there is only one subgroup of G of order ##p^k## which is G itself. Does this means that any group of order ##p^k##, with p prime is cyclic?

    Thank you!
     
  2. jcsd
  3. Nov 17, 2016 #2

    fresh_42

    Staff: Mentor

    Which other finite Abelian groups do you know which are not cyclic?
     
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