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

Author(s): Patrick Simonetta
Journal: Proc. Amer. Math. Soc. 131 (2003), 3913-3917.
MSC (2000): Primary 03C60; Secondary 20F18
Posted: March 25, 2003
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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.

References:

1.
D. Haskell, H. D. Macpherson, Cell decomposition of $C$-minimal structures, Annals of Pure and Applied Logic 66 (1994), 113-162. MR 95d:03059

2.
D. Haskell, E. Hrushovski, H. D. Macpherson, Definable sets in algebraically closed valued fields. Part I: elimination of imaginaries, submitted.

3.
A. A. Ivanov, H. D. Macpherson, Strongly determined types, Annals of Pure and Applied Logic 99 (1999), 197-230. MR 2000j:03050

4.
L. Lipshitz, Z. Robinson, One-dimensional fibers of rigid subanalytic sets, J. Symbolic Logic 63 (1998), 83-88. MR 98m:32049

5.
H. D. Macpherson, C. Steinhorn, On variants of o-minimality, Annals of Pure and Applied Logic 79 (1996), 165-209. MR 97e:03050

6.
P. Ribenboim, The Theory of Classical Valuations, Springer, Berlin 1998. MR 2000d:12007

7.
P. Simonetta, Abelian $C$-minimal groups, Annals of Pure and Applied Logic 110 (2001), 1-22. MR 2002g:03083

8.
P. Simonetta, On non-abelian $C$-minimal groups, to appear in Annals of Pure and Applied Logic.

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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: 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
Posted: March 25, 2003
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2003, American Mathematical Society

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