We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into classifying spaces of nilpotent groups. We use a modified Bousfield–Kan homology completion tower zkX whose terms we prove are all X–cellular for any X . As straightforward consequences, we show that if X is K–acyclic and ...

We prove Beurling's theorem and L p − L q Morgan's theorem for step two nilpotent Lie groups. These two theorems together imply a group of uncertainty theorems.

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...

Image at right: Olga Taussky−Todd in her Caltech office circa 1960, wearing the famous "numbers" dress Abstract: Skew-symmetric tridiagonal Bohemian matrices with population P = [1,i] have eigenvalues some interesting properties. We explore of these here, and I prove a theorem showing that only possible dimensions where nilpotent can occur are one less than power two. explicitly give set this f...

in this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. with this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. n(g) and s(g) are the set of all nilpotency classes and the set of all solvability classes for the group g with respect to different automorphi...