On supersimple groups

Cédric Milliet (1, 2)

1 ICJ - Institut Camille Jordan
2 GSU - Université Galatasaray

An infinite group with supersimple theory has a finite series of definable groups whose factors are infinite and either virtually-FC or virtually-simple modulo a finite FC-centre. A group which is type-definable in a supersimple theory has a finite series of relatively definable groups whose factors are either abelian or simple groups. In this decomposition, the non-abelian simple factors are unique up to isomorphism.

Mots clés: Model theory; supersimple group; just-infinite groups; series with abelian or simple factors

Domaines: Logique [math.LO]

Cédric Milliet. On supersimple groups. Journal of Algebra, 2013, 373, pp.426-438. ⟨10.1016/j.jalgebra.2012.09.033⟩. ⟨hal-00703511v2⟩