  The generalised Fitting subgroup of a finite group is the group generated by
all subnormal subgroups that are either nilpotent or quasisimple. The
importance of this subgroup in finite group theory stems from the fact that it
always contains its own centraliser, so that any finite group is an abelian
extension of a group of automorphisms of its generalised Fitting subgroup. We
define a class of profinite groups which generalises this phenomenon, and
explore some consequences for the structure of profinite groups.
