Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups

Asked Jul 19 '16 at 13:10

Active Jul 19 '16 at 13:16

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Let $L\subset \mathbb{Z}$ be the subgroup of $\mathbb{Z}^3$ generated by the elements $(-1,-1,4),(2,4,0),(3,3,8)$. Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups.

I've tried creating a matrix and row reducing, finding the null space of the matrix, but it doesn't seem to produce an obvious answer.

Any help greatly appreciated!

edited Jul 19 '16 at 13:16

user26857

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asked Jul 19 '16 at 13:10

Jess

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Have you tried to use https://en.wikipedia.org/wiki/Smith_normal_form? – user26857 Jul 19 '16 at 13:16
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Questions very similar to this one have been asked many times. Here are a few: 1, 2, 3. – Viktor Vaughn Jul 20 '16 at 14:55

Write $\mathbb{Z}^3/L$ as a direct sum of cyclic groups

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