On torsion-free groups in o-minimal structures

On torsion points of locally definable groups in o-minimal structures

In this paper we study the structure of m-torsion points of connected locally definable abelian groups in o-minimal expansions of fields. ∗Supported by the FCT grant SFRH/BPD/6015/2001 while a post-doctoral research fellow at the Mathematical Institute, University of Oxford. MSC: 03C64; 20E99.

Groups Definable in O-minimal Structures

In this series of lectures, we will a) introduce the basics of ominimality, b) describe the manifold topology of groups definable in o-minimal structures, and c) present a structure theorem for the special case of semi-linear groups, exemplifying their relation with real Lie groups. The structure of these lectures is as follows: (1) Basics of o-minimality: definition, Cell Decomposition Theorem...

Solvable groups definable in o-minimal structures

Let N be an o-minimal structure. In this paper we develop group extension theory over N and use it to describe N -definable solvable groups. We prove an o-minimal analogue of the Lie-Kolchin-Mal’cev theorem and we describe N -definable G-modules and N -definable

Definably Simple Groups in O-minimal Structures

Let G = 〈G, ·〉 be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure 〈G, ·〉 (while definable means definable in the structure M). Assume G has no Gdefinable proper subgroup of finite index. In this paper we prove that if G has no nontrivial abelian normal subgroup, then G is the direct product of G-definable subgroups H1, . . . ,Hk s...

Permutation groups in o-minimal structures