Figure 4

Matrices illustrate the four Abelian groups for a twenty-state alphabet. (a) the {\mathbb{Z}}_2\times {\mathbb{Z}}_2\times {\mathbb{Z}}_5 group, (b) {\mathbb{Z}}_4\times {\mathbb{Z}}_5, (c) {\mathbb{Z}}_2\times {\mathbb{Z}}_{10}, and (d) {\mathbb{Z}}_{20}. Each matrix visualizes the cosets of the subgroups of the depicted group and suggests an associated grouping of the 20 states.