Hello,
I have a group $\displaystyle G=(\mathbb{R}^{2},+)$ and it's subgroup $\displaystyle H=\{{(x,y) \in \mathbb{R}^{2}: x+3y=0\}$. What are the elements of quotient group $\displaystyle G / H$? How to find them?
Hi MachinePL1993!
The elements of a quotient group are cosets, which are of the form (a + H) for an additive group.
In your case $\displaystyle a$ is point in $\displaystyle \mathbb{R}^{2}$ and H is your line.
When we add a point to a line, we get a parallel line.
So G/H consists of all lines parallel to H.