On the Algebraic Structure of Gaussian Periods Original Research Article

We show that the classical cyclotomic constants associated to a primepand a positive integerndividingp−1 can be used to define an algebraic object which we call an assembly and which is close to being a finite commutative hypergroup. We study these objects abstractly and show that subject to a condition of cyclical symmetry they are determined uniquely by two quantities which we call total mass and order. This shows that the theory of cyclotomy can in some sense be viewed as a chapter of abstract algebra.