Topological Quasi-Group Shifts

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In this work we characterize those shift spaces which can support a 1-block quasi-group operation and show the analogous of Kitchens result: any such shift is conjugated to a product of a full shift with a finite shift. Moreover, we prove that every expansive automorphism on a compact zero-dimensional quasi-group that verifies the medial property, commutativity and has period 2, is isomorphic to the shift map on a product of a finite quasi-group with a full shift.