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ON THE STRUCTURE OF GROUPS ENDOWED WITH A COMPATIBLE C-RELATION

Published online by Cambridge University Press:  23 October 2018

GABRIEL LEHÉRICY
GABRIEL LEHÉRICY*
Affiliation:
FACHBEREICH MATHEMATIK UND STATISTIK UNIVERSITÄT KONSTANZ 78457 KONSTANZ, GERMANY and UNIVERSITÉ PARIS DIDEROT INSTITUT DE MATHÉMATIQUES DE JUSSIEU - PARIS RIVE GAUCHE (IMJ-PRG) 75013 PARIS, FRANCE E-mail: [email protected]
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Abstract

We use quasi-orders to describe the structure of C-groups. We do this by associating a quasi-order to each compatible C-relation of a group, and then give the structure of such quasi-ordered groups. We also reformulate in terms of quasi-orders some results concerning C-minimal groups given in [5].

Keywords

13A1820F6006F1503C60ordered groupvaluationC-minimalityquasi-order
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 3 , September 2018 , pp. 939 - 966
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

REFERENCES

Adeleke, S. A. and Neumann, P. M., Primitive permutation groups with primitive Jordan sets. Journal of the London Mathematical Society, vol. 53 (1996), no. 2, pp. 209–229.CrossRefGoogle Scholar
Adeleke, S. A. and Neumann, P. M., Relations related to betweenness: Their structure and their automorphisms, Memoirs of the American Mathematical Society, Vol. 623, American Mathematical Society, Providence, RI, 1998.Google Scholar
Delon, F., C-minimal structures without the density assumption, Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry (Cluckers, R., Nicaise, J., and Sebag, J., editors), Cambridge University Press, Berlin, 2011, pp. 51–86.CrossRefGoogle Scholar
Lehéricy, G., A structure theorem for abelian quasi-ordered groups, Journal of Pure and Applied Algebra, to appear.Google Scholar
Macpherson, D. and Steinhorn, C., On variants of o-minimality. Annals of Pure and Applied Logic, vol. 79 (1996), pp. 165–209.CrossRefGoogle Scholar
Simonetta, P., Abelian C-minimal groups. Annals of Pure and Applied Logic, vol. 110 (2001), no. 1–3, pp. 1–22.CrossRefGoogle Scholar
Simonetta, P., On non-abelian C-minimal groups. Annals of Pure and Applied Logic, vol. 122 (2003), pp. 263–287.CrossRefGoogle Scholar