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Consider the integral matrix

$$R = \left(\begin{matrix} 2 & 4 & 6 & -8 \\ 1 & 3 & 2 & -1 \\ 1 & 1 & 4 & -1 \\ 1 & 1 & 2 & 5 \end{matrix}\right).$$

Determine the structure of the abelian group given by generators and relations.

$$A_r = \{a_1, a_2, a_3, a_4 | R \circ \vec{a} = 0\}$$

I know you have to row/column reduce the matrix however am unsure what to do next.

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    I tried to fix some formatting, but I'm not sure what the $A_r = \ldots$ should be. I hope it currently says what you meant.2012-05-13
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    Its meant to be < > but it wouldnt show up2012-05-13
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    The question [here](http://math.stackexchange.com/questions/133076/computing-the-smith-normal-form/133178#133178) is similar. The answer I gave there may help you get started.2012-05-13

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