Skip to Main content Skip to Navigation

Propriétés combinatoires et modèle-théoriques des groupes

Abstract : Our work here relates to certain routes for the construction of new groups, and in particular, of counter-examples to the Cherlin-Zilber conjecture. We managed to find an answer for the stability of existentially closed CSA- groups. We build a group word in two variables that has the independence property relatively to the class of torsion-free hyperbolic groups. We deduced that the corresponding equation gives the independence property of existentially closed CSA groups which in turn implies their instability. Moreover, we demonstrate that group words, and in particular quantifierfree definable sets, define stable sets in bounded balls of free products of groups using a finite version of Ramsey’s theorem. Finally, we introduce certain groups constructed as special towers of free products and HNN-extensions.
Document type :
Complete list of metadatas

Cited literature [62 references]  Display  Hide  Download
Contributor : Abes Star :  Contact
Submitted on : Thursday, March 15, 2012 - 4:02:20 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
Long-term archiving on: : Monday, June 18, 2012 - 4:21:12 PM


Version validated by the jury (STAR)


  • HAL Id : tel-00679429, version 1


Azadeh Neman. Propriétés combinatoires et modèle-théoriques des groupes. Mathématiques générales [math.GM]. Université Claude Bernard - Lyon I, 2009. Français. ⟨NNT : 2009LYO10098⟩. ⟨tel-00679429⟩



Record views


Files downloads