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Groups of order p^2

  1. Dec 7, 2009 #1
    1. The problem statement, all variables and given/known data
    If the order of G is p^2 and p is prime, then show that G is either cyclic or isomorphic to ZpXZp...

    2. Relevant equations

    3. The attempt at a solution
    Any hints here will help!
  2. jcsd
  3. Dec 7, 2009 #2
    I think two helpful facts here is that if the |G|=p2 for prime p, then G has non-trivial Centre. Furthermore, the Normalizer of the group is greater than the Centre. You can use this to show that the Centre of G is the entire group G, which implies it is abelian. Then use some other theorems involving abelian groups to prove your theorem.
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