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 the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...

let h be a subgroup of a group g. h is said to be s-embedded in g if g has a normal t such that ht is an s-permutable subgroup of g and h ∩ t ≤ h sg, where h denotes the subgroup generated by all those subgroups of h which are s-permutable in g. in this paper, we investigate the influence of minimal s-embedded subgroups on the structure of finite groups. we determine the structure the finite grou...