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Preimage of arbitrary subgroup.

  1. Apr 27, 2014 #1
    Suppose θ: A → B is a homomorphism. And assume S ≤ B. Is it necesarily true that if S is a subgroup, that is not completely contained in the range, its preimage forms a subgroup?
     
  2. jcsd
  3. Apr 27, 2014 #2
    Thoughts?
     
  4. Apr 27, 2014 #3
    I used subgroup criterion test, and it should be a subgroup. But i just wanted to make sure I didn't miss anything trivial.
     
  5. Apr 27, 2014 #4
    You didn't. It's a subgroup indeed!
     
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