Let $a, b, c, d, e, f, g$ denote integers, with $a$ and $c$ both non-zero, and consider the matrix $$ M=\left(\begin{matrix} a&b&d&f \\ 0&c&e&g \end{matrix}\right) $$ Let $G$ be the quotient of the group $\Bbb Z^2$ by the column space of $M$. That is, $G$ is presented by two generators, say ...

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