A geometric approach to the almost convexity and growth of some nilpotent groups

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Download Full-text

Computer Modeling of a Tire under Cornering Loads

Tire Science and Technology ◽

10.2346/1.2141681 ◽

1989 ◽

Vol 17 (2) ◽

pp. 86-99 ◽

Cited By ~ 4

Author(s):

I. Gardner ◽

M. Theves

Keyword(s):

Finite Element Analysis ◽

Geometric Approach ◽

Lateral Force ◽

Slip Angle ◽

Element Analysis ◽

Pressure Distributions ◽

Slip Effects ◽

Improved Accuracy ◽

Nonlinear Geometric ◽

Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

Download Full-text

Geometric approach to nondestructive identification of faults in stochastic structural systems

AIAA Journal ◽

10.2514/3.13568 ◽

1997 ◽

Vol 35 ◽

pp. 700-705

Author(s):

M. H. Sadeghi ◽

S. D. Fassois

Keyword(s):

Geometric Approach ◽

Structural Systems ◽

Nondestructive Identification

Download Full-text

Linear Transformations, Projection Operators and Generalized Inverses; A Geometric Approach

10.21236/ada197608 ◽

1988 ◽

Author(s):

C. R. Rao

Keyword(s):

Geometric Approach ◽

Generalized Inverses ◽

Projection Operators ◽

Linear Transformations

Download Full-text

Quantum mechanics and nilpotent groups. I: The curved magnetic field

Publications of the Research Institute for Mathematical Sciences ◽

10.2977/prims/1195178792 ◽

1985 ◽

Vol 21 (5) ◽

pp. 969-999 ◽

Cited By ~ 16

Author(s):

Palle E.T. Jørgensen ◽

William H. Klink

Keyword(s):

Magnetic Field ◽

Quantum Mechanics ◽

Nilpotent Groups

Download Full-text

Powerfully nilpotent groups of rank 2 or small order

Journal of Group Theory ◽

10.1515/jgth-2020-0016 ◽

2020 ◽

Vol 23 (4) ◽

pp. 641-658

Author(s):

Gunnar Traustason ◽

James Williams

Keyword(s):

Detailed Analysis ◽

Special Kind ◽

Nilpotent Groups ◽

Nilpotency Class ◽

Central Series ◽

Rank 2 ◽

Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

Download Full-text