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Find:2 Non-isomorphic groups of order n squared. help?

  1. Mar 10, 2005 #1
    Find:2 Non-isomorphic groups of order n squared

    i think that Zn X Zn is one.

    Can you help me find another.


    Thanks
     
  2. jcsd
  3. Mar 10, 2005 #2

    Galileo

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    Isomorphic to what?
     
  4. Mar 10, 2005 #3
    nonisomorphic means not isomorphic to each other, doesn't it? like the klein 4-group & Z_4 both have order 2^2 but are nonisomorphic

    since K_4 = Z_2 x Z_2 i conjecture off the cuff that the 2 nonisomorphic groups with order n^2 would be Z_n x Z_n and Z_(n^2)
     
    Last edited: Mar 10, 2005
  5. Mar 10, 2005 #4
    If you mean non-isomorphic to each other, then you can take Z_(n^2) and Z_n x Z_n, for example (under addition).

    In response to the above post: Indeed, those work, since Z_(n^2) is cyclic but Z_n x Z_n is not (you can see this alternatively in terms of vector spaces: dim(Z_(n^2)) = 1 but dim(Z_n x Z_n) = 2)
     
    Last edited: Mar 10, 2005
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