Examples of Groups


Book Description




Basic Notions of Algebra


Book Description

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.




Groups and Characters


Book Description

Group representation theory is both elegant and practical, with important applications to quantum mechanics, spectroscopy, crystallography, and other fields in the physical sciences. This book offers an easy-to-follow introduction to the theory of groups and of group characters. Designed as a rapid survey of the subject, it emphasizes examples and applications of the theorems, and avoids many of the longer and more difficult proofs. The text includes sections that provide the mathematical basis for some of the applications of group theory. It also offers numerous exercises, some stressing computation of concrete examples, others stressing development of the theory.




Kleinian Groups and Uniformization in Examples and Problems


Book Description

Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of powerful new methods in topology, the theory of functions of several complex variables, and the theory of quasiconformal mappings. Thus this new book should provide a valuable resource, listing the basic facts regarding Kleinian groups and serving as a general guide to the primary literature, particularly the Russian literature in the field. In addition, the book includes a large number of examples, problems, and unsolved problems, many of them presented for the first time.




Self-Similar Groups


Book Description

Self-similar groups (groups generated by automata) initially appeared as examples of groups that are easy to define but have exotic properties like nontrivial torsion, intermediate growth, etc. This book studies the self-similarity phenomenon in group theory and shows its intimate relationship with dynamical systems and more classical self-similar structures, such as fractals, Julia sets, and self-affine tilings. This connection is established through the central topics of the book, which are the notions of the iterated monodromy group and limit space. A wide variety of examples and different applications of self-similar groups to dynamical systems and vice versa are discussed. In particular, it is shown that Julia sets can be reconstructed from the respective iterated monodromy groups and that groups with exotic properties can appear not just as isolated examples, but as naturally defined iterated monodromy groups of rational functions. The book offers important, new mathematics that will open new avenues of research in group theory and dynamical systems. It is intended to be accessible to a wide readership of professional mathematicians.




Some Examples of Groups


Book Description




The Dynamics of Ethnic Competition and Conflict


Book Description

This study of ethnic violence in the United States from 1877 to 1914 reveals that not all ethnic groups were equally likely to be victims of violence; the author seeks the reasons for this historical record. This analysis of the causes of urban racial and ethnic strife in large American cities at the turn of the century should comprise important empirical and theoretical reference material for social scientists and historians alike.




Introduction to Group Theory


Book Description

This book quickly introduces beginners to general group theory and then focuses on three main themes : finite group theory, including sporadic groups combinatorial and geometric group theory, including the Bass-Serre theory of groups acting on trees the theory of train tracks by Bestvina and Handel for automorphisms of free groups With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples. Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.




Dietary Reference Intakes


Book Description

The Dietary Reference Intakes (DRIs) are quantitative estimates of nutrient intakes to be used for planning and assessing diets for apparently healthy people. This volume is the second of two reports in the DRI series aimed at providing specific guidance on the appropriate uses of the DRIs. The first report provided guidance on appropriate methods for using DRIs in dietary assessment. This volume builds on the statistical foundations of the assessment report to provide specific guidance on how to use the appropriate DRIs in planning diets for individuals and for groups. Dietary planning, whether for an individual or a group, involves developing a diet that is nutritionally adequate without being excessive. The planning goal for individuals is to achieve recommended and adequate nutrient intakes using food-based guides. For group planning, the report presents a new approach based on considering the entire distribution of usual nutrient intakes rather than focusing on the mean intake of the group. The report stresses that dietary planning using the DRIs is a cyclical activity that involves assessment, planning, implementation, and reassessment. Nutrition and public health researchers, dietitians and nutritionists responsible for the education of the next generation of practitioners, and government professionals involved in the development and implementation of national diet and health assessments, public education efforts and food assistance programs will find this volume indispensable for setting intake goals for individuals and groups.




Ansible Linux Users & Groups By Examples


Book Description

Learn the Ansible automation technology with some real-life examples. Every successful IT department needs automation nowadays for bare metal servers, virtual machines, could, containers, and edge computing. Automate your IT journey with Ansible automation technology. I'm going to teach you example by example how to manage users and groups in Linux and macOS operation systems are the most common System Administrator tasks. Each of the 20+ lessons summarizes a specific scenario about user and groups management: creating a user, creating a new pair of a suitable SSH key and a home directory, changing a password and specifying the encryption cipher, removing the home directory and the mailbox, or assigning a special `nologin` shell for temporarily disabled users. Another user scenario that happens very often is when you need only to temporarily disable and enable a user. Another useful administrator tool is group management to assign permission to resources to a bunch of users. You could easily customize the example code with your username and use it in your everyday journey without any additional effort. There are some Ansible codes usable in all the Linux systems, battle-tested for RedHat-like and Debian-like systems. Are you ready to automate your day with Ansible? Examples in the book are tested with the latest version of Ansible 2.9+ and Ansible Core 2.11+.