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Normal Subgroups

  1. Apr 23, 2009 #1
    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.
  2. jcsd
  3. Apr 23, 2009 #2


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    Hint: { ... -4, -2, 0, 2, 4 ... } is isomorphic to { ... -2, -1, 0, 1, 2, ... }.
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