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Thread: Need help with a factor group

  1. #1
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    Need help with a factor group

    Giventhe group (Z24, +). Consider the subgroup U={ [0]24,[4]24,[8]24,[12]24,[16]24,[20]24}.Determine the elements of Z24/U .
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    Re: Need help with a factor group

    Quote Originally Posted by uniculdan View Post
    Giventhe group (Z24, +). Consider the subgroup U={ [0]24,[4]24,[8]24,[12]24,[16]24,[20]24}.Determine the elements of Z24/U .
    Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$
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    Re: Need help with a factor group

    Quote Originally Posted by Plato View Post
    Surely you know that the elements of $\mathbb{Z}_{24}/U$ are just the cosets of $U$ in $\mathbb{Z}_{24}~?$
    Here is the original text.Need help with a factor group-factor.jpg
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    Re: Need help with a factor group

    Quote Originally Posted by uniculdan View Post
    Here is the original text.Click image for larger version. 

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    Even from the German, it is not clear to me form of the answer your textbook/instructor wants.
    Can you give us the element $11+[12]_{24}~?$

    Can you give us the coset $11+U~?$
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    Re: Need help with a factor group

    [12]24={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]24={...-49, -25, -1, 33, 47, 71...}=[23]24
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    Re: Need help with a factor group

    Quote Originally Posted by uniculdan View Post
    [12]24={...-60, -36, -12, 12, 36, 60,...}. So 11+[12]24={...-49, -25, -1, 33, 47, 71...}=[23]24
    Well done! Now tell us why you cannot finish the exercise?
    Thanks from uniculdan
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