Definably simple groups in o-minimal structures

Authors:
Y. Peterzil, A. Pillay and S. Starchenko

Journal:
Trans. Amer. Math. Soc. **352** (2000), 4397-4419

MSC (2000):
Primary 03C64, 22E15, 20G20; Secondary 12J15

DOI:
https://doi.org/10.1090/S0002-9947-00-02593-9

Published electronically:
February 24, 2000

MathSciNet review:
1707202

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Abstract | References | Similar Articles | Additional Information

Let be a group definable in an o-minimal structure . A subset of is -definable if is definable in the structure (while *definable* means definable in the structure ). Assume has no -definable proper subgroup of finite index. In this paper we prove that if has no nontrivial abelian normal subgroup, then is the direct product of -definable subgroups such that each 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.

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Additional Information

**Y. Peterzil**

Affiliation:
Department of Mathematics and Computer Science, Haifa University, Haifa, Israel

Email:
kobi@mathcs2.haifa.ac.il

**A. Pillay**

Affiliation:
Department of Mathemetics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61801

Email:
pillay@math.uiuc.edu

**S. Starchenko**

Affiliation:
Department of Mathemetics, University of Notre Dame, Room 370, CCMB, Notre Dame, Indiana 46556

Email:
starchenko.1@nd.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02593-9

Received by editor(s):
February 25, 1998

Published electronically:
February 24, 2000

Additional Notes:
The second and the third authors were partially supported by NSF

Article copyright:
© Copyright 2000
American Mathematical Society