A Fitting Theorem for Simple Theories
  The Fitting subgroup of a type-definable group in a simple theory is relatively definable and nilpotent. Moreover, the Fitting subgroup of a supersimple hyperdefinable group has a normal hyperdefinable nilpotent subgroup of bounded index, and is itself of bounded index in a hyperdefinable subgroup. 
Daniel Palacin, Frank Olaf Wagner (ICJ)
math.LO math.GR