The aim of this paper is to prove Theorem 1.1 below, a generalization to virtually nilpotent spaces of a result of Wilkerson [13] and Sullivan [12]. We recall that a CW complex Y is virtually nilpotent if (i) Y is connected, (ii) 7r~ Y is virtually nilpotent (i.e. has a nilpotent subgroup of finite index) and (iii) for every integer n > 1, zr~Y has a subgroup of finite index which acts nilpoten...

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 ...

A nilpotent group G is a finite group that is the direct product of its Sylow p-subgroups. Theorem 1.1 (Fitting's Theorem) Let G be a finite group, and let H and K be two nilpotent normal subgroups of G. Then HK is nilpotent. Hence in any finite group there is a unique maximal normal nilpotent subgroup, and every nilpotent normal subgroup lies inside this; it is called the Fitting subgroup, and...

The notion of a multiplier of a group X is generalized to that of a C-multiplier by allowing it to have values in an arbitrary C-algebra A. On the other hand, the notion of the action of X in A is generalized to that of a projective action of X as linear transformations of the space of continuous functions with compact support in X and with values in A. It is shown that there exists a one-to-on...

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...

In this study, a C~K band frequency synthesizer used in broadband electronic warfare equipment was designed, developed, and the measurement results were presented. The structure of designed generates signal up to 6 GHz using only direct digital synthesizer(DDS) without mixer or multiplier. For signals above frequency, uses addition, variable sampling DDS circuit improve quality by reducing spur...

Introduction. Let G be a Lie group and M a compact C manifold. In [2] Anosov actions of G on M are defined and proved to be structurally stable. In this announcement we are concerned with the foliation ^ of M defined by the orbits of G. Under the assumption that G is connected, # is C stable (3). If G is connected and nilpotent, G has a compact orbit (4). If G is merely solvable, however, there...

JCHPS Special Issue 8: December 2016 www.jchps.com Page 9 Design of Low-Power Specific Parallel Array Multipliers C Vivek*, R. Subalakshmi Department of Electronics and Communication Engineering, M. Kumarasamy College of Engineering, Karur, Tamil Nadu. *Corresponding author: E-Mail: [email protected] ABSTRACT Multipliers play a critical part in recent digitalized life. In this advanced spher...

Remark 1.2. Uniform exponential growth for solvable non-virtually nilpotent groups was proved independently by Osin and byWilson. The existence of a uniform constant C(d) as in Theorem 1.1 for solvable groups is very striking since it implies the well known Lehmer conjecture concerning the Mahler measure of algebraic integers. However for virtually solvable non-virtually nilpotent groups we onl...

A group is said to have the R∞ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R∞ property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n ≥ 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point ...