2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79664To a given Pisot unit $β$ we associate a finite abelian group whose size appears to be equal to the discriminant of $β$. We call it the Pisot group and find its representation in the two-sided $β$-compactum in the case of $β$ satisfying the relation $Fin(β)=\Bbb Z[β]\cap[0,1)$. 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 $β$.10 pages in AMS-TeXNumber TheoryDynamical Systems11R06; 28D05; 58F03text