Cosets

The product group (Z_m×Z_n, +) contains subgroups H=<S> generated by zero or more elements. The left cosets and right cosets of H coincide because (Z_m×Z_n, +) is Abelian.

The cells of the array correspond to elements of . Click one or more cells to add elements to S; the elements of H=<S> are highlighted.

At any stage you may “freeze” the subgroup H under consideration and investigate its cosets. Once H is frozen, clicking a cell (a, b) highlights elements of the coset (a, b)+H in a different color.

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

m = n =