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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Commutators in groups definable in o-minimal structures


Authors: Elías Baro, Eric Jaligot and Margarita Otero
Journal: Proc. Amer. Math. Soc. 140 (2012), 3629-3643
MSC (2010): Primary 03C64; Secondary 20F12, 20F38, 20A15, 03C60
Published electronically: February 27, 2012
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Abstract: We prove the definability and actually the finiteness of the commutator width of many commutator subgroups in groups definable in o-minimal structures. This applies in particular to derived series and to lower central series of solvable groups. Along the way, we prove some generalities on groups with the descending chain condition on definable subgroups and/or with a definable and additive dimension.


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Additional Information

Elías Baro
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Address at time of publication: Universidad Complutense de Madrid, 28040 Madrid, Spain

Eric Jaligot
Affiliation: Institut Fourier, CNRS, Université Grenoble I, 100 rue des maths, BP 74, 38402 St Martin d’Hères cedex, France

Margarita Otero
Affiliation: Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11209-2
PII: S 0002-9939(2012)11209-2
Keywords: Commutators, o-minimality, semi-algebraic groups, Lie groups.
Received by editor(s): February 23, 2011
Received by editor(s) in revised form: April 9, 2011, and April 16, 2011
Published electronically: February 27, 2012
Additional Notes: The three authors are partially supported by MTM2011-22435. The first and third authors are partially supported by Grupos UCM 910444/GR35/10-A
Communicated by: Julia Knight
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.