multiplicative primitive residue class group

A modulo multiplication group is a finite group M_m of residue classes prime to m under multiplication mod m. M_m is Abelian of group order ϕ(m), where ϕ(m) is the totient function. A modulo multiplication group can be visualized by constructing its cycle graph. Cycle graphs are illustrated above for some low-order modulo multiplication groups. Such graphs are constructed by drawing labeled nodes, one for each element A of the residue class, and connecting cycles obtained by iterating A^n. Each edge of such a graph is bidirected, but they are commonly drawn using undirected edges with double edges used to indicate cycles of length two (Shanks 1993, pp. 85 and 87-92).

characteristic factor | cycle graph | finite group | quadratic residue | residue class