Let G = R² with operation the addition of pairs, and let H={(x, 0): x∈R}. what is the quotient group G/H.
I know that one is H itself, but I don’t know how to find the others.
Notice that $\displaystyle H \cong \mathbb{R} \times \{ 0\}$ and so $\displaystyle G/H \cong \frac{ \mathbb{R} \times \mathbb{R} }{ \mathbb{R} \times \{ 0\} } \cong \left( \mathbb{R} / \mathbb{R} \right) \times \left( \mathbb{R} / \{ 0\} \right) \cong \{ 0\} \times \mathbb{R} \cong \mathbb{R}$