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Definable envelopes of nilpotent subgroups of groups with chain conditions on centralizers


Authors: Tuna Altınel and Paul Baginski
Journal: Proc. Amer. Math. Soc. 142 (2014), 1497-1506
MSC (2010): Primary 20F22, 03C60
DOI: https://doi.org/10.1090/S0002-9939-2014-11879-X
Published electronically: February 4, 2014
MathSciNet review: 3168457
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Abstract: An $ \mathfrak{M}_C$ group is a group in which all chains of centralizers have finite length. In this article, we show that every nilpotent subgroup of an $ \mathfrak{M}_C$ group is contained in a definable subgroup which is nilpotent of the same nilpotence class. Definitions are uniform when the lengths of chains are bounded.


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Tuna Altınel
Affiliation: Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France
Email: altinel@math.univ-lyon1.fr

Paul Baginski
Affiliation: Institut Camille Jordan, Université Claude Bernard Lyon 1, Lyon, France 69622
Address at time of publication: Department of Mathematics, Fairfield University, 1073 North Benson Road, Fairfield, Connecticut 06824
Email: pbaginski@fairfield.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11879-X
Keywords: Group theory, nilpotence, chains of centralizers, model theory, definability
Received by editor(s): October 17, 2011
Received by editor(s) in revised form: March 26, 2012, and May 29, 2012
Published electronically: February 4, 2014
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.