## Abstract

We continue the investigation of infinite, definably simple groups which are definable in o-minimal structures. In Definably simple groups in o-minimal structures, we showed that every such group is a semialgebraic group over a real closed field. Our main result here, stated in a model theoretic language, is that every such group is either bi-interpretable with an algebraically closed field of characteristic zero (when the group is stable) or with a real closed field (when the group is unstable). It follows that every abstract isomorphism between two unstable groups as above is a composition of a semialgebraic map with a field isomorphism. \Ve discuss connections to theorems of Freudenthal, Borel-Tits and Weisfeiler on automorphisms of real Lie groups and simple algebraic groups over real closed fields.

Original language | English |
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Pages (from-to) | 4421-4450 |

Number of pages | 30 |

Journal | Transactions of the American Mathematical Society |

Volume | 352 |

Issue number | 10 |

DOIs | |

State | Published - 2000 |

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics