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Math Help - How to describe this abelian group denoted by G

  1. #1
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    How to describe this abelian group denoted by G

    G=(Z+Z+Z)/N where Z denote the integers and + is direct sum and
    N = <(7,8,9), (4,5,6), (1,2,3)> or the smallest submodule of Z+Z+Z containing these 3 vectors.

    How would you describe G?

    One could use a presentation to describe G which in this case is G = <a,b,c |7a+8b+9c=0, 4a+5b+6c=0, a+2b+3c=0> where a,b,c are the standard basis vectors for R^3.

    However I do not know what G looks like in this form either.

    One way to look at G is G=X/(q:X->X)

    where X is R^3. q is the linear transformation given by the transformation matrix
    A=
    7 4 1
    8 5 2
    9 6 3

    But what does this form of G look like?


    In other words I do not know what any of the 3 forms of G looks like.
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  2. #2
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    You question was answered. Here.
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