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The Algebra of Quadratic Residues


     

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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 Ck occurs the same number γijk of times among the elements which result on combining each element of Ci with each element of Cj 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.
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  • The Algebra of Quadratic Residues

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Abstract


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 Ck occurs the same number γijk of times among the elements which result on combining each element of Ci with each element of Cj 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.