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Math Help - unable to understand cosets

  1. #1
    xyz
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    unable to understand cosets

    The definition of coset is as follows



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





    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.
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  2. #2
    xyz
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    another example

    Another example would be



    i don't understand it
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  3. #3
    Master Of Puppets
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    Quote Originally Posted by xyz View Post
    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?
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  4. #4
    xyz
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    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}?
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  5. #5
    Senior Member Shanks's Avatar
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    and 4=0 because 4 and 0 represent the same element in Z_4 Group.
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