Some results on the classification of expansive automorphisms of compact Abelian groups

In this paper we study expansive automorphisms of compact O-dimensional abelian groups. Our main result is the complete algebraic and topological classification of the transitive expansive automorpisms for which the maximal order of the elements is p(2) for a prime p. This yields a classification of the transitive expansive automorphisms with topological entropy log p(2). Finally, we prove a necessary and sufficient condition for an expansive automorphism to be conjugated, topologically and algebraically, to a shift over a finite group.