Definably simple groups in O-minimal structures

Y. Peterzil, A. Pillay, S. Starchenko

Research output: Contribution to journalArticlepeer-review


Let G = 〈G1 ·〉 be a group definable in an o-minimal structure M.. A subset // of G is G-definable if H is definable in the structure 〈G1 ·〉 (while definable means definable in the structure M). Assume G has no G-definable proper subgroup of finite index. In this paper We prove that if G has no nontrivial abelian normal subgroup, then G is the direct product of G-definable subgroups H1,... ,Hk such that each Hi is definably isomorphic to a semialgebraic linear group over a definable real closed field. As a corollary we obtain an o-minimal analogue of Cherlin's conjecture.

Original languageEnglish
Pages (from-to)4397-4419
Number of pages23
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - 2000

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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