A Fitting Theorem for Simple Theories
arXiv:1410.2583 · doi:10.1112/blms/bdw018
Abstract
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.