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Math Help - quotient group

  1. #1
    Junior Member
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    quotient group

    Let G = with operation the addition of pairs, and let H={(x, 0): xR}. what is the quotient group G/H.
    I know that one is H itself, but I don’t know how to find the others.
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  2. #2
    Super Member
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    Notice that H \cong \mathbb{R} \times \{ 0\} and so G/H \cong \frac{ \mathbb{R} \times \mathbb{R} }{ \mathbb{R} \times \{ 0\} } \cong \left( \mathbb{R} / \mathbb{R} \right) \times \left( \mathbb{R} / \{ 0\} \right) \cong \{ 0\} \times \mathbb{R} \cong \mathbb{R}
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