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Équations génériques dans un groupe stable nilpotent

Published online by Cambridge University Press:  12 March 2014

Khaled Jaber*
Affiliation:
Institut Girard Desargues, Upres-A5028 Mathématiques, Université Claude Bernard Lyon1, 43, Boulevard Du 11 Novembre 1918, 69622 Villeurbanne Cedex, France E-mail: [email protected]

Abstract

We prove that in a nilpotent-by-finite stable group an equation that holds generically holds everywhere. Combining this result with results of Wagner and Bryant, we conclude that a soluble-by-finite stable group of generic exponent n has exponent n.

Résumé

Résumé

On prouve que dans un groupe stable, nilpotent par fini, une équation générìquement satisfaite y est partout satisfaite. En combinant ce résultat avec des résultats de Wagner et Bryant, on déduit qu'un groupe stable résoluble-par-fini d'exposant généríque n est d'exposant n.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1] Borovik, Alexandre V. and Nesin, Ali, Groups of Finite Morley Rank, Oxford University Press, 1994.CrossRefGoogle Scholar
[2] Bryant, Roger M. and Hartley, B., Periodic locally soluble groups with the minimal condition on centralisers, Journal of Algebra, vol. 61 (1979), pp. 328334.CrossRefGoogle Scholar
[3] Corredor, L.J., Bad groups of finite Morley rank, this Journal, vol. 54 (1989), pp. 768773.Google Scholar
[4] Khukhro, Evgenii I., Nilpotent groups and their automorphisms, Walter de Gruyter, Berlin, New York, 1993.CrossRefGoogle Scholar
[5] Poizat, Bruno, Groupes Stables, Nur Al-Mantiq wal-Ma'rifah, Villeurbanne, France, 1987.Google Scholar
[6] Poizat, Bruno, Équations génériques, Proceedings of the Eighth Easter Conference on model theory (Berlin) (Dahn, B. and Wolter, H., editors), Humboldt-Universität, 1990, pp. 131138.Google Scholar
[7] Poizat, Bruno and Wagner, Frank, Sous-groupes périodiques d'un groupe stable, this Journal, vol. 58 (1993), no. 2, pp. 385400.Google Scholar
[8] Wagner, Frank, Stable Groups, Cambridge University Press, 1997.CrossRefGoogle Scholar
[9] Wagner, Frank O., À propos d'équations génériques, this Journal, vol. 57 (1992), no. 2, pp. 548554.Google Scholar