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

 

An example of a $C$-minimal group which is not abelian-by-finite


Author: Patrick Simonetta
Journal: Proc. Amer. Math. Soc. 131 (2003), 3913-3917
MSC (2000): Primary 03C60; Secondary 20F18
Published electronically: March 25, 2003
MathSciNet review: 1999940
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Abstract: In 1996 D. Macpherson and C. Steinhorn introduced $C$-minimality as an analogue, for valued fields and some groups with a definable chain of normal subgroups with trivial intersection, of the notion of o-minimality. One of the open questions of that paper was the existence of a non abelian-by-finite $C$-minimal group. We give here the first example of such a group.


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Additional Information

Patrick Simonetta
Affiliation: Equipe de Logique Mathématique, Université de Paris VII, 2, place Jussieu - case 7012, 75251 Paris cedex 05, France
Email: simbaud@logique.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06969-7
PII: S 0002-9939(03)06969-7
Keywords: $C$-minimal groups, $C$-minimality, o-minimality, algebraically closed valued fields, nilpotent groups
Received by editor(s): May 25, 2001
Received by editor(s) in revised form: July 25, 2002
Published electronically: March 25, 2003
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2003 American Mathematical Society