Fitting's theorem

Fitting's theorem is a mathematical theorem proved by Hans Fitting.

[1] 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 (including all finite groups) is nilpotent.

However, a subgroup generated by an infinite collection of nilpotent normal subgroups need not be nilpotent.

[3] This abstract algebra-related article is a stub.