Does Preimage of Subgroup Under Homomorphism Form a Subgroup?

xiavatar · Apr 27, 2014

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?

micromass · Apr 27, 2014

Thoughts?

xiavatar · Apr 27, 2014

I used subgroup criterion test, and it should be a subgroup. But i just wanted to make sure I didn't miss anything trivial.

micromass · Apr 27, 2014

xiavatar said:

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!

Does Preimage of Subgroup Under Homomorphism Form a Subgroup?

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Does Preimage of Subgroup Under Homomorphism Form a Subgroup?

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