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Math Help - Prove H=mZ

  1. #1
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    Prove H=mZ

    Let H be a subgroup of (\mathbb{Z},+) with more than one element, and let m be the smallest positive integer in H \cap \mathbb{N}. Prove that H=m\mathbb{Z}. [Hint: Use the Division Algorithm]

    Question: Does m\mathbb{Z} look like this:

    m\mathbb{Z}=\{0, \pm m, \pm 2m, \pm3m, \cdot \cdot \cdot\}?
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  2. #2
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    Quote Originally Posted by novice View Post
    Let H be a subgroup of (\mathbb{Z},+) with more than one element, and let m be the smallest positive integer in H \cap \mathbb{N}. Prove that H=m\mathbb{Z}. [Hint: Use the Division Algorithm]

    Question: Does m\mathbb{Z} look like this:

    m\mathbb{Z}=\{0, \pm m, \pm 2m, \pm3m, \cdot \cdot \cdot\}?

    Yes.

    Tonio
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