Abstract
To a given Pisot unitwe associate a finite abelian group whose size appears to be equal to the discriminant of �. We call it the Pisot group and find its representation in the two-sided �-compactum in the case ofsatisfying the relation Fin(�) = Z(�) (0,1). As a motivation for the definition, we show that the Pisot group is the kernel of some important arithmetic coding of the toral automorphism given by the companion matrix naturally associated with �.
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