The structure of compact connected groups which admit an expansive automorphism

Abstract

1. Remark We will make extensive use of the Pontryagin Duality Theory for compact abelian and discrete abelian groups. This material can be found in [17, Chapter 5] and in [12, Chapter 6]. We also assume a knowledge of torsion free rank for discrete abelian groups as described in [12, Appendix A]. When we use the term rank we mean torsion free rank. In particular, we use the following fact: ^ 2. Theorem. Let G be a compact abelian group and let G be the character groUp of G. Then the dimension of G is equal to ^ tNe rank of G.