# unable to understand cosets

• Nov 22nd 2009, 07:45 PM
xyz
unable to understand cosets
The definition of coset is as follows

http://i291.photobucket.com/albums/l...apture8475.jpg

However, I am still not able to understand what this means. An example shown is

http://i291.photobucket.com/albums/l...apture4395.jpg

I do not understand how 3 + H = {3, 1}. 3 does not belong in H. and I also don't understand 2+H = {2, 0}.

I can't make out much from the textbook. Where can I learn this material? I would like to see some more simplified and friendly defintion. In fact for past couple of hours I am struggling to get a grasp on cosets.
• Nov 22nd 2009, 07:58 PM
xyz
another example
Another example would be

http://i291.photobucket.com/albums/l...apture7676.jpg

i don't understand it
• Nov 22nd 2009, 07:59 PM
pickslides
Quote:

Originally Posted by xyz
I do not understand how 3 + H = {3, 1}. 3 does not belong in H. and I also don't understand 2+H = {2, 0}.

I can't make out much from the textbook. Where can I learn this material? I would like to see some more simplified and friendly defintion. In fact for past couple of hours I am struggling to get a grasp on cosets.

It says H = {0,2}

so adding the element 1 to subgroup H to make a left co-set gives 1+H = {1,3} as one is added to each element of H e.g {0+1,2+1} = {1,3}

as follows 2+H = 2+{0,2} = {0+2,2+2} = {2,0}

Does this help?
• Nov 22nd 2009, 08:13 PM
xyz
Okay, its supposed to be 2+H = 2+{0,2} = {0+2,2+2} = {2,0}. However, isn't 2+2 = 4? so shouldn't it be {2, 4}?
• Nov 22nd 2009, 08:23 PM
Shanks
and 4=0 because 4 and 0 represent the same element in Z_4 Group.