Wednesday, 21 August 2013

List all elements of quotient group $ G / H $.

List all elements of quotient group $ G / H $.

List all elements of quotient group $ G / H $ and explain operation. I
solved $ 7 $ examples and it's nice, but I don't know how I must solve
these two examples. $$ i) \ G = (\mathbb{R}^2, +), H = \{ (x, y) \in
\mathbb{R}^2: x + 3y = 0\} $$ $$ ii) \ G = (\mathbb{R}^3, +), H =
\{(x,y,z) \in \mathbb{R}^3 : x + y + z = 0 \} $$ Could you show me, how I
must consider them?

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