Periodic ordered permutation groups and cyclic orderings
It is shown that periodic ordered permutation groups satisfying certain extra conditions are very nearly simple. This is applied to several natural examples, such as the following. (i) If \(z\) denotes the map \(x \mapsto x + 1\) on \(\mathbb{R}\), and \(\text{Diff}(\mathbb{R})\) is the group of diffeomorphisms of \(\mathbb{R}\), then \(C_{\text{Diff}(\mathbb{R})}(\langle z \rangle)/\langle z \rangle\) is simple. (ii) The automorphism group of the countable homogeneous local order (one of the three countable homogeneous tournaments) is simple. Also, an extension of Rieger's Theorem is given, relating groups of automorphisms of cyclic orderings to groups of automorphisms of total orderings.
scientific article; zbMATH DE number 767697