论文信息 - Groups of Dimension Two and Three Over o-Minimal Structures

Groups of Dimension Two and Three Over o-Minimal Structures

Abstract Let G be a group definable in an o-minimal structure M . In this paper we show: Theorem . If G is a two-dimensional definably connected nonabelian group, then G is centerless and G is isomorphic to R + ⋊ R ∗ > 0 , for some real closed field R . Theorem . If G is a three-dimensional nonsolvable, centerless, definably connected group, then either G ≅ SO 3 ( R ) or G ≅ PSL 2 ( R ), for some real closed field R .

Anand Pillay | Ali Nesin | Vladimir Razenj

[1] Anand Pillay,et al. On groups and fields definable in o-minimal structures , 1988 .

[2] A. Pillay,et al. DEFINABLE SETS IN ORDERED STRUCTURES. I , 1986 .

[3] Vladimir Razenj. On-Dimensional Groups over an o-Minimal Structure , 1991, Ann. Pure Appl. Log..

[4] Gregory Cherlin. Groups of small Morley rank , 1979 .

[5] A. Pillay,et al. Definable sets in ordered structures , 1984 .

[6] Anand Pillay,et al. Some model theory of compact Lie groups , 1991 .

[7] Anand Pillay. First Order Topological Structures and Theories , 1987, J. Symb. Log..

[8] Lou van den Dries,et al. Algebraic Theories with Definable Skolem Functions , 1984, J. Symb. Log..

[9] Ali Nesin,et al. Non-solvable groups of Morley rank 3 , 1989 .

[10] Anand Pillay. Some Remarks on Definable Equivalence Relations in O-Minimal Structures , 1986, J. Symb. Log..