The Algebra of Quadratic Residues

In a recent paper I shewed that the classes C₁,C₂,... into which the elements of a group G fall with respect to any group of automorphisms of G, combine among themselves by the group-operation in the sense that each element of any class C_k occurs the same number γ_ij^k of times among the elements which result on combining each element of C_i with each element of C_j by the group-operation. A simple case of this general principle was studied in the paper referred to, namely the classes of a cyclic group with respect to its total group of automorphisms. The present paper is devoted to another simple case of the same principle.