Linear groups definable in o-minimal structures

Y. Peterzil, A. Pillay, S. Starchenko

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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.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Algebra
Issue number1
StatePublished - 1 Jan 2002

Bibliographical note

Funding Information:
1Supported by NSF grant. 2Supported by NSF grant.

ASJC Scopus subject areas

  • Algebra and Number Theory


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