Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-24T21:42:03.639Z Has data issue: false hasContentIssue false
  • English
  • Français

On ω-categorical, generically stable groups

Published online by Cambridge University Press:  12 March 2014

Jan Dobrowolski  and
Krzysztof Krupiński
Jan Dobrowolski
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: Jan.Dobrowolski@math.uni.wroc.pl
Krzysztof Krupiński
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: kkrup@math.uni.wroc.pl
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that each ω-categorical, generically stable group is solvable-by-finite.

Keywords

ω-categorical groupgenerically stable type
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 3 , September 2012 , pp. 1047 - 1056
Copyright
Copyright © Association for Symbolic Logic 2012

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.)

References

REFERENCES

[1] Baur, W., Cherlin, G., and Macintyre, A., Totally categorical groups and rings, Journal of Algebra, vol. 57 (1979), pp. 407–440.Google Scholar
[2] Ealy, C., Krupiński, K., and Pillay, A., Superrosy dependent groups having finitely satisfiable generics, Annals of Pure and Applied Logic, vol. 151 (2008), pp. 1–21.CrossRefGoogle Scholar
[3] Evans, D. and Wagner, F., Supersimple ω-categorical groups and theories, this Journal, vol. 65 (2000), pp. 767–776.Google Scholar
[4] Hrushovski, E. and Pillay, A., On NIP and invariant measures, Journal of the European Mathematical Society, vol. 13 (2011), pp. 1005–1061.Google Scholar
[5] Hrushovski, E., Pillay, A., and Peterzil, Y., Groups, measures, and the NIP, Journal of the American Mathematical Society, vol. 21 (2008), pp. 563–595.Google Scholar
[6] Krupiński, K., On ω-categorical groups and rings with NIP, Proceedings of the American Mathematical Society, vol. 140 (2012), pp. 2501–2512.CrossRefGoogle Scholar
[7] Macpherson, H. D., Absolutely ubiquitous structures and ℕ0-categorical groups, Quarterly Journal of Mathematics, vol. 39 (1988), pp. 483–500.Google Scholar
[8] Pillay, A. and Tanović, P., Generic stability, regularity, and quasi-minimality, preprint, 2009.Google Scholar
[9] Poizat, B., Stable groups, American Mathematical Society, Providence, 2001.Google Scholar
[10] Wilson, J., The algebraic structure of ω-categorical groups, Groups-St. Andrews (Campbell, C. M. and Robertson, E. F., editors), London Mathematical Society Lecture Notes 71, Cambridge, 1981, pp. 345–358.Google Scholar