Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: February 24, 2000
MathSciNet review: 1707202
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

Let $\mathbb{G} =\langle G, \cdot\rangle$ be a group definable in an o-minimal structure $\mathcal{M}$. A subset $H$ of $G$ is $\mathbb{G} $-definable if $H$ is definable in the structure $\langle G,\cdot\rangle$(while definable means definable in the structure $\mathcal{M}$). Assume $\mathbb{G} $ has no $\mathbb{G} $-definable proper subgroup of finite index. In this paper we prove that if $\mathbb{G} $has no nontrivial abelian normal subgroup, then $\mathbb{G} $ is the direct product of $\mathbb{G} $-definable subgroups $H_1,\ldots,H_k$ such that each $H_i$ 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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03C64, 22E15, 20G20, 12J15

Retrieve articles in all journals with MSC (2000): 03C64, 22E15, 20G20, 12J15


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: http://dx.doi.org/10.1090/S0002-9947-00-02593-9
PII: S 0002-9947(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