Generated Subgroups

The product group $(\mathbf{Z}_{m} \times \mathbf{Z}_{n}, +)$ contains subgroups $\langle S \rangle$ generated by zero or more elements.

The cells of the array correspond to elements of . Click a cell to add that element to $\langle S \rangle$; the elements of $\langle S \rangle$ are highlighted.

Select $m$ and $n$, then click the button to generate a new group. (Maximum size is .)

$m = $ $n = $