Abstract Algebra

  • Thread starter BurrowK
  • Start date
  • #1
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

  • #2
morphism
Science Advisor
Homework Helper
2,015
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
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!
 

Related Threads on Abstract Algebra

  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
5
Views
786
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
17
Views
3K
  • Last Post
Replies
1
Views
875
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
1K
Top