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Group Theory Problem

  1. Oct 29, 2007 #1


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    I'm stuck on this one...

    I'm studying for my midterm so I'm solving problems for practice. Here's one of them...

    Let H be a normal subgroup in G, and let v be the natural map from G to G/H, and let X be a subset of G such that the subgroup generated by v(X) is G/H. Prove that the subgroup generated by H union X (HuX) is G.

    I'm trying to do this directly with showing if x is in G, then x is in <HuX> (generated subgroup). I tried doing contradiction too, by assuming <HuX> is some proper subgroup A of G and not G itself.

    I'm going to spend more time thinking about this. I'll be back in like 2 hours since I have a meeting, which I'll spend a minute here or there thinking about it.
  2. jcsd
  3. Oct 29, 2007 #2


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    What's the pullback of <v(X)>?
  4. Oct 29, 2007 #3


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    Good thought!

    Not sure where it will lead me, but I'll think about that too.
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