Groups of dimension two and three over o-minimal structures

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Annals of Pure and Applied Logic 53 (3):279-296 (1991)
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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 SO3 or G PSL2, for some real closed field R

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10.1016/0168-0072(91)90025-h

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Citations of this work

One-dimensional groups over an o-minimal structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
Intersection theory for o-minimal manifolds.Alessandro Berarducci & Margarita Otero - 2001 - Annals of Pure and Applied Logic 107 (1-3):87-119.
An open mapping theorem for o-minimal structures.Joseph Johns - 2001 - Journal of Symbolic Logic 66 (4):1817-1820.

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References found in this work

First order topological structures and theories.Anand Pillay - 1987 - Journal of Symbolic Logic 52 (3):763-778.
Algebraic theories with definable Skolem functions.Lou van den Dries - 1984 - Journal of Symbolic Logic 49 (2):625-629.
One-dimensional groups over an o-minimal structure.Vladimir Razenj - 1991 - Annals of Pure and Applied Logic 53 (3):269-277.
Groups of small Morley rank.Gregory Cherlin - 1979 - Annals of Mathematical Logic 17 (1):1.

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