• Support PF! Buy your school textbooks, materials and every day products Here!

Normal Subgroups

  • Thread starter zcdfhn
  • Start date
  • #1
23
0
Prove or disprove:

Suppose N is a normal subgp of G and N' is a normal subgp of G'. If G is isomorphic to G' and N is isomorphic to N' does that mean that G/N is isomorphic to G'/N'?

I was trying to work out a proof until my professor told us to think of subgroups of the integers when doing this problem. So now I'm trying to disprove it through a counterexample. I have been stuck on this question for a while and I would appreciate any help.

Thank you.
 

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
2,011
18
Hint: { ... -4, -2, 0, 2, 4 ... } is isomorphic to { ... -2, -1, 0, 1, 2, ... }.
 

Related Threads for: Normal Subgroups

Replies
0
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
795
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
847
  • Last Post
Replies
2
Views
883
Top