Topology Proceedings SEMIGROUP CONJECTURES FOR CENTRAL SEMIDIRECT PRODUCT OF R WITH R
نویسندگان
چکیده
In this paper we prove two new results about closed semigroups in the family of solvable groups Hmn := R nφ R where φ, the structure homomorphism, maps nontrivially into the center of Aut(Rn). The rst result states that the closure of a semigroup generated by a set in Hmn that is not included in a maximal semigroup with nonempty interior is actually a group. The second result states that among the sets in Hmn that are not included in a maximal proper semigroup, those that generate Hmn as a closed semigroup are dense. Results of this nature were obtained before only for extensions of nilpotent groups. An application of our results is to the question of generic topological transitivity of skew-extensions of a hyperbolic system with ber Hmn. 2010 Mathematics Subject Classi cation. Primary 22A15, 54H15; Secondary 22A25.
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