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Équations génériques dans un groupe stable nilpotent

Published online by Cambridge University Press:  12 March 2014

Khaled Jaber
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: jaber@desargues.univ-lyonl.fr
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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
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 761 - 768
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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