Realizations of rotations on an indecomposable compact monothetic group

Abstract

By the classical Halmos‐von Neumann theorem, each compact monothetic group corresponds to an ergodic dynamical system with discrete spectrum. For such groups we prove two results. We first construct a compact monothetic group which does not split into a direct product of a connected and a totally disconnected compact monothetic group. Then we present a measure preserving dynamical system on the unit square being isomorphic to a rotation on this indecomposable group.

A Study in Locally Compact Groups—Chabauty Space, Sylow Theory, the Schur-Zassenhaus Formalism, the Prime Graph for Near Abelian Groups

“…We begin with a definition elaborating the definition of near abelian groups. In Example 4.2, the group G is a subgroup of R/Z and is a construction due to D. Maier [34]. Example 4.3 is inspired by Example ∇ in Theorem A1.32, p. 686 of [20].…”