Isomorphisms problem homework

  • Thread starter Benzoate
  • Start date
  • #1
420
0

Homework Statement



Prove or disprove U(20) and U(24) are isomorphic

Homework Equations





The Attempt at a Solution



U(20)={1,3,,7,9,11,13,17,19}
U(24)={1,5,7,11,13,17,19}

In U(20), Order(1)=1 Order(3)=4 Order(7)=4 Order(9)=2, Order(11)=2 Order(13)=4, Order(17)=4, Order(19)=2

In U(24), Order(1)= 1 , Order(5)=2 , ORder(7)=2, Order(11)=2 , Order(13)=2 , Order(17)=2, Order(19)= 2

Since each of the elements in each of the groups do not generate the same order for each elements in the opposite group, can't I conclude thatt U(24) and U(20) are not isomorphic?
 

Answers and Replies

  • #2
morphism
Science Advisor
Homework Helper
2,015
4
You can say that U(24) has 6 elements of order 2, while U(20) doesn't. So they certainly can't be isomorphic.

(By the way, you're missing 23 in U(24). So in fact U(24) has 7 elements of order 2, but this is immaterial.)
 
Last edited:

Related Threads on Isomorphisms problem homework

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
1
Views
1K
Replies
3
Views
4K
  • Last Post
Replies
1
Views
699
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
1
Views
855
  • Last Post
Replies
24
Views
2K
  • Last Post
Replies
3
Views
2K
Top