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Linear Groups Definable in o-Minimal Structures

✍ Scribed by Y. Peterzil; A. Pillay; S. Starchenko

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
156 KB
Volume
247
Category
Article
ISSN
0021-8693

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✦ Synopsis

We study subgroups G of GL n, R definable in o-minimal expansions M s Ž . Ž. R, q, и , . . . 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 Ž . 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.

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