Topological Conjugation Classes of Tightly Transitive Subgroups of Homeo+(S1)

Let Homeo + ( S 1 ) denote the group of orientation preserving homeomorphisms of the circle S 1 . A subgroup G of Homeo + ( S 1 ) is tightly transitive if it is topologically transitive and no subgroup H of G with [ G : H ] = ∞ has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of Homeo + ( S 1 ) which are isomorphic to Z n for any integer n ≥ 2 .