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.
CITATION STYLE
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
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