Elements of quotient groups

**MachinePL1993** · March 17th 2013, 09:15 AM

Hello,
I have a group $G=(\mathbb{R}^{2},+)$ and it's subgroup $H=\{{(x,y) \in \mathbb{R}^{2}: x+3y=0\}$ . What are the elements of quotient group $G / H$ ? How to find them?

**ILikeSerena** · March 17th 2013, 03:03 PM

Originally Posted by MachinePL1993

Hello,
I have a group $G=(\mathbb{R}^{2},+)$ and it's subgroup $H=\{{(x,y) \in \mathbb{R}^{2}: x+3y=0\}$ . What are the elements of quotient group $G / H$ ? 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 $a$ is point in $\mathbb{R}^{2}$ 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.

Thread: Elements of quotient groups

LinkBack

Thread Tools

Display

Elements of quotient groups

Re: Elements of quotient groups

Similar Math Help Forum Discussions

Groups: determining elements with polynomials

Groups of 44 elements

Quotient ring and field of 9 elements

Quotient Groups - Infinite Groups, finite orders

Orders of elements in Symmetric groups

Search Tags