Fitting's theorem
Fitting's theorem is a mathematical theorem proved by Hans Fitting. It can be stated as follows:
By induction it follows also that the subgroup generated by a finite collection of nilpotent normal subgroups is nilpotent. This can be used to show that the Fitting subgroup of certain types of groups is nilpotent. However, a subgroup generated by an infinite collection of nilpotent normal subgroups need not be nilpotent.