We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces.We define homotopy n-nilpotent groups as homotopy algebras over certain simplicial algebraic theories.This notion interpolates between infinite loop spaces and loop spaces, but backwards.We study the relation to ordinary nilpotent groups.We prove that n-excisive functors of the form F factor over the category of homotopy n-nilpotent groups.
