Linear groups definable in o-minimal structures

33Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

We study subgroups G of GL(n, R) definable in o-minimal expansions M = (R, +,·,...) of a real closed field R. We prove several results such as: (a) G can be defined using just the field structure on R together with, if necessary, power functions, or an exponential function definable in M. (b) If G has no infinite, normal, definable abelian subgroup, then G is semialgebraic. We also characterize the definably simple groups definable in o-minimal structures as those groups elementarily equivalent to simple Lie groups, and we give a proof of the Kneser-Tits conjecture for real closed fields. © 2002 Elsevier Science.

Cite

CITATION STYLE

APA

Peterzil, Y., Pillay, A., & Starchenko, S. (2002). Linear groups definable in o-minimal structures. Journal of Algebra, 247(1), 1–23. https://doi.org/10.1006/jabr.2001.8861

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free