On supersimple groups

International audienceAn 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

Propriétés résiduelles dans les groupes supersimples (Residual properties in supersimple groups)

International audienceIf \C is a pseudo-variety, then a supersimple residually \C group is nilpotent-by-poly-\C. Si \C est une pseudo-variété, alors un groupe supersimple résiduellement \C est nilpotent-par-poly-\C