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
Full-text PDF
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