Solvable groups definable in o-minimal structures

By Mário J. Edmundo. 2000

50 citations recorded by the source corpus.

Abstract In this paper we develop group extension theory over an o-minimal structure 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 rings.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d49a4236196f434ae272721bf739a49f01872151

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Ehud Hrushovski
2. Anand Pillay
3. Ya'acov Peterzil

In Geometry and Topology

1. Ehud Hrushovski
2. Anand Pillay
3. Ya'acov Peterzil
4. Hans Adler
5. Pierre Simon
6. Terence Tao
7. Emmanuel Breuillard
8. Ben Joseph Green

In Mathematical Physics

1. Ehud Hrushovski
2. Anand Pillay
3. Ya'acov Peterzil
4. Hans Adler
5. Jacob Tsimerman
6. Jonathan Pila
7. Pierre Simon
8. Bruno Klingler

Citations in the corpus

• On central extensions and definably compact groups in o-minimal structures (2008, background): “Note that by [5], the structure M has definable choice functions for subsets of A × G, hence there exists a definable set of representatives X ⊆ A×G2r and a definable bijection α : G̃ → X.”