Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-20T18:56:21.358Z Has data issue: false hasContentIssue false
  • English
  • Français

The model theory of finitely generated finite-by-abelian groups

Published online by Cambridge University Press:  12 March 2014

Francis Oger
Francis Oger*
Affiliation:
Université ParisVII, Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

In [O1], we gave algebraic characterizations of elementary equivalence for finitely generated finite-by-abelian groups, i.e. finitely generated FC-groups. We also provided several examples of finitely generated finite-by-abelian groups which are elementarily equivalent without being isomorphic.

In this paper, we shall use our previous results to describe precisely the models of the theories of finitely generated finite-by-abelian groups and the elementary embeddings between these models.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 49 , Issue 4 , December 1984 , pp. 1115 - 1124
Copyright
Copyright © Association for Symbolic Logic 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[CK]Chang, C. C. and Keisler, H. J., Model theory, Studies in Logic and the Foundations of Mathematics, vol. 73, North-Holland, Amsterdam, 1973.Google Scholar
[F]Felgner, U., The model theory of FC-groups, Mathematical Logic in Latin America (Arruda, A., Chuaqui, R. and da Costa, N., editors), Studies in Logic and the Foundations of Mathematics, vol. 99, North-Holland, Amsterdam, 1980, pp. 163–190.Google Scholar
[GPS]Grünewald, F. J., Pickel, P. F. and Segal, D., Polycyclic groups with isomorphic finite quotients, Annals of Mathematics, ser. 2, vol. 111 (1980), pp. 155–195.CrossRefGoogle Scholar
[O1]Oger, F., Équivalence élémentaire entre groupes finis-par-abéliens de type fini, Commentarii Mathematici Helvetici, vol. 57 (1982), pp. 469–480.CrossRefGoogle Scholar
[O2]Oger, F., Des groupes nilpotents de classe 2 sans torsion de type fini ayant les mêmes images finies peuvent ne pas être élémentairement équivalents, Comptes Rendus de l'Académie des Sciences. Série 1: Mathématique, vol. 294 (1982), pp. 1–4.Google Scholar
[R]Robinson, D., Finiteness conditions and generalized soluble groups, Ergebnisse der Mathematik und Ihrer Grenzgebiete, vol. 62, Springer-Verlag, Berlin and New York, 1972.Google Scholar
[S]Shelah, S., Classification theory and the number of nonisomorphic models, Studies in Logic and the Foundations of Mathematics, vol. 92, North-Holland, Amsterdam, 1978.Google Scholar
[W]Warfield, R. B., Nilpotent groups, Lecture Notes in Mathematics, vol. 513, Springer-Verlag, Berlin and New York, 1976.CrossRefGoogle Scholar