the theory of classes of groups mathematics and its applications

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The Theory Of Classes Of Groups

Author : Guo Wenbin
ISBN : 9789401140546
Genre : Mathematics
File Size : 79. 41 MB
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One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.

Classes Of Finite Groups

Author : Adolfo Ballester-Bollinches
ISBN : 9781402047190
Genre : Mathematics
File Size : 89. 14 MB
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This book covers the latest achievements of the Theory of Classes of Finite Groups. It introduces some unpublished and fundamental advances in this Theory and provides a new insight into some classic facts in this area. By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups.

Introduction To Group Theory With Applications

Author : Gerald Burns
ISBN : 9781483191492
Genre : Mathematics
File Size : 80. 65 MB
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Introduction to Group Theory with Applications covers the basic principles, concepts, mathematical proofs, and applications of group theory. This book is divided into 13 chapters and begins with discussions of the elementary topics related to the subject, including symmetry operations and group concepts. The succeeding chapters deal with the properties of matrix representations of finite groups, the vibrations of molecular and crystals, vibrational wave function, selection rules, and molecular approximations. These topics are followed by reviews of the basic of quantum mechanics, crystal field theory, atomic physics, hybrid functions, and molecular orbital theory. The last chapters describe the symmetry of crystal lattices, the band theory of solids, and the full rotation group. This book will be of value to undergraduate mathematics and physics students.

Symmetry

Author : R. McWeeny
ISBN : 9781483226248
Genre : Mathematics
File Size : 90. 2 MB
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Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.

Structure Theory For Canonical Classes Of Finite Groups

Author : Wenbin Guo
ISBN : 9783662457474
Genre : Mathematics
File Size : 24. 15 MB
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This book offers a systematic introduction to recent achievements and development in research on the structure of finite non-simple groups, the theory of classes of groups and their applications. In particular, the related systematic theories are considered and some new approaches and research methods are described – e.g., the F-hypercenter of groups, X-permutable subgroups, subgroup functors, generalized supplementary subgroups, quasi-F-group, and F-cohypercenter for Fitting classes. At the end of each chapter, we provide relevant supplementary information and introduce readers to selected open problems.

Proceedings Of The First Jamaican Conference On Group Theory And Its Applications

Author : Tuval Shmuel Foguel
ISBN : CORNELL:31924065495669
Genre : Mathematics
File Size : 75. 7 MB
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Group Theory With Applications In Chemical Physics

Author : Patrick Jacobs
ISBN : 1139445197
Genre : Science
File Size : 20. 50 MB
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Group Theory is an indispensable mathematical tool in many branches of chemistry and physics. This book provides a self-contained and rigorous account on the fundamentals and applications of the subject to chemical physics, assuming no prior knowledge of group theory. The first half of the book focuses on elementary topics, such as molecular and crystal symmetry, whilst the latter half is more advanced in nature. Discussions on more complex material such as space groups, projective representations, magnetic crystals and spinor bases, often omitted from introductory texts, are expertly dealt with. With the inclusion of numerous exercises and worked examples, this book will appeal to advanced undergraduates and beginning graduate students studying physical sciences and is an ideal text for use on a two-semester course.

Group Theory In China

Author : Zhexian Wan
ISBN : 0792339894
Genre : Mathematics
File Size : 58. 43 MB
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Hsio-Fu Tuan is a Chinese mathematician who has made important contributions to the theories of both finite groups and Lie groups. He has also had a great influence on the development of algebra, and particularly group theory in China. The present volume consists of a collection of essays on various aspects of group theory written by some of his former students and colleagues in honour of his 80th birthday. The papers contain the main general results, as well as recent ones, on certain topics within this discipline. The chief editor, Zhe-Xian Wan, is a leading algebraist in China.

Mathematics Galore

Author : Christopher Budd
ISBN : 0198507704
Genre : Juvenile Nonfiction
File Size : 32. 28 MB
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This book is a series of self-contained workshops in mathematics which aim to enthuse and inspire young people, their parents and teachers with the joy and excitement of modern mathematics. Written in an informal style, each chapter describes how novel mathematical ideas relate directly to real life. The chapters contain both a description of the mathematics and its applications together with problem sheets, their solutions and ideas for further work, project and field trips. Topics include; mazes, folk dancing, sundials, magic, castles, codes, number systems, and slide rules. This book should be accessible to young people from age thirteen upwards and yet contains material which should stretch the brightest students.

Group Theory And Its Application To Physical Problems

Author : Morton Hamermesh
ISBN : 9780486140391
Genre : Science
File Size : 38. 59 MB
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One of the best-written, most skillful expositions of group theory and its physical applications, directed primarily to advanced undergraduate and graduate students in physics, especially quantum physics. With problems.

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