On supersimple groups

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