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Thread: abstract algebra - group theory

  1. #1
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    abstract algebra - group theory

    Need help on this. i dont understand the whole equation.abstract algebra - group theory-pcq1-q3.gif I've found some resources that helped me to understand this equation .
    Last edited by noobpronoobpro; Sep 14th 2017 at 05:56 AM.
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    Re: abstract algebra - group theory

    Quote Originally Posted by noobpronoobpro View Post
    Need help on this. i dont understand the whole equation.Click image for larger version. 

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    It means that the number $2+_{12}x+_{12}7\equiv 1$. When the LHS is divided by $12$ the remainder is $1$.
    The what is $x~?$
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    Re: abstract algebra - group theory

    Blast! I wrote out an answer but my internet connection went down before I could post it!

    " Z_{12}" is the set of integers "modulo 12". That is, we consider two integers whose difference is a multiple of 12 to be the same. and " +_{12}" is "addition modulo 12". " 7+_{12} 2= 9" because 9 is less than 12 but 7+ 8+_{12}= 3 because 7+ 8= 15= 12+ 3. Here, 2+_{12} x+_{12}+ 7= x+_{12} 9= 1 is the same as x= 1-_{12} 9= -8= -12+ 4= 4 (mod 12).
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