Preimage of arbitrary subgroup.

  • Thread starter xiavatar
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  • #1
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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?
 

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  • #2
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Thoughts?
 
  • #3
100
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I used subgroup criterion test, and it should be a subgroup. But i just wanted to make sure I didn't miss anything trivial.
 
  • #4
22,089
3,297
I used subgroup criterion test, and it should be a subgroup. But i just wanted to make sure I didn't miss anything trivial.

You didn't. It's a subgroup indeed!
 

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