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Groups of order p^2 where p is prime

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data
    let p be a prime number and let G be a group with order p^2. the task is to show that G is either cyclic or isomorphic to Zp X Zp.
    a. let a, not equal to the identity,be an element in G and A=<a>. What's the order of A.
    b. consider the cosets of A: G/A={A,g2A,...gnA}. What's the value of n?


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    3. The attempt at a solution
    for part a, does the order of A have to do with the index of A in G? If so, how?
    for part b, can i use the fact that the index of A divides the order of G? If so, how?
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    3. The attempt at a solution
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    3. The attempt at a solution
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  2. jcsd
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