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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: [email protected]
Krzysztof Krupiński
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland, E-mail: [email protected]
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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

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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