交换群 Smith normal form

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UTM Armstrong  groups and symmetry Exercise 22.2
交换群有5个生成元, 4个线性关系, 系数矩阵为\begin{bmatrix}3&-4&5&3&7\\
3&2&-1&-3&1\\
8&2&-2&-8&2\\
11&-8&9&-5&9\end{bmatrix}群同构于$ℤ_2\timesℤ_6\timesℤ_6\timesℤ$.

证明:

1. SmithDecomposition[{{3,-4,5,3,7},{3,2,-1,-3,1},{8,2,-2,-8,2},{11,-8,9,-5,9}}]

Copy the Code

\begin{bmatrix}
1 & 0 & 0 & 0 & 0 \\
0 & 2 & 0 & 0 & 0 \\
0 & 0 & 6 & 0 & 0 \\
0 & 0 & 0 & 6 & 0 \\
\end{bmatrix}