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Homework Help: Abstract Algebra

  1. Mar 16, 2008 #1
    I'm going insane. The question is:
    List all abelian groups (up to isomorphism) of order 144.

    There are 10 non-isomorphic groups of order 144 and I only have 9. Here they are:

    Z2 X Z2 X Z2 X Z2 X Z3 X Z3
    Z2 X Z2 X Z2 X Z2 X Z9
    Z4 X Z2 X Z2 X Z3 X Z3
    Z4 X Z2 X Z2 X Z9
    Z8 X Z2 X Z3 X Z3
    Z8 X Z2 X Z9
    Z4 X Z4 X Z3 X Z3
    Z4 X Z4 X Z9
    Z16 X Z3 X Z3

    (with the isomorphism being Z16 X Z9)

    Anyone? Bueller?
    Last edited: Mar 16, 2008
  2. jcsd
  3. Mar 16, 2008 #2


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    What do you mean by this statement? Z16 x Z9 gives a distinct isomorphism class - it's precisely the one you're missing.
  4. Mar 17, 2008 #3
    Yeah, I realised that that counted towards the 10. It's the midst of finals so the brain's on the fritz. I was just going to take this post down, thanks though!
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