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Abstract Algebra

  • Thread starter BurrowK
  • Start date
3
0
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:

Answers and Replies

morphism
Science Advisor
Homework Helper
2,013
4
(with the isomorphism being Z16 X Z9)
What do you mean by this statement? Z16 x Z9 gives a distinct isomorphism class - it's precisely the one you're missing.
 
3
0
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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