Books in Group theory and generalizations

Group Representations

1st Edition
Volume 2
June 6, 2016
Gregory Karpilovsky
English
eBook
9 7 8 1 4 8 3 2 9 5 0 9 1

This second volume deals with projective representations and the Schur multiplier. Some further topics pertaining to projective representations will be covered in the next volume. The bibliography is extensive, leading the reader to various references for detailed discussions on the main topics as well as on related subjects.

Group Representations

1st Edition
Volume 4
June 6, 2016
Gregory Karpilovsky
English
eBook
9 7 8 1 4 8 3 2 9 5 1 0 7

This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings.The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.

Semihypergroup Theory

1st Edition
June 2, 2016
Bijan Davvaz
English
Paperback
9 7 8 0 1 2 8 0 9 8 1 5 8
eBook
9 7 8 0 1 2 8 0 9 9 2 5 4

Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject.

Regular Figures

1st Edition
July 10, 2014
L. Fejes Tóth
I. N. Sneddon + 2 more
English
eBook
9 7 8 1 4 8 3 1 5 1 4 3 4

Regular Figures concerns the systematology and genetics of regular figures. The first part of the book deals with the classical theory of the regular figures. This topic includes description of plane ornaments, spherical arrangements, hyperbolic tessellations, polyhedral, and regular polytopes. The problem of geometry of the sphere and the two-dimensional hyperbolic space are considered. Classical theory is explained as describing all possible symmetrical groupings in different spaces of constant curvature. The second part deals with the genetics of the regular figures and the inequalities found in polygons; also presented as examples are the packing and covering problems of a given circle using the most or least number of discs. The problem of distributing n points on the sphere for these points to be placed as far as possible from each other is also discussed. The theories and problems discussed are then applied to pollen-grains, which are transported by animals or the wind. A closer look into the exterior composition of the grain shows many characteristics of uniform distribution of orifices, as well as irregular distribution. A formula that calculates such packing density is then explained. More advanced problems such as the genetics of the protean regular figures of higher spaces are also discussed. The book is ideal for physicists, mathematicians, architects, and students and professors in geometry.

Computational Problems in Abstract Algebra

1st Edition
May 17, 2014
John Leech
English
eBook
9 7 8 1 4 8 3 1 5 9 4 2 3

Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing with things like generation of permutations, projective planes, orthogonal latin squares, graphs, difference sets, block designs, and Hadamard matrices. Comprised of 35 chapters, this book begins with an overview of the methods utilized in and results obtained by programs for the investigation of groups. This text then examines the method for establishing the order of a finite group defined by a set of relations satisfied by its generators. Other chapters describe the modification of the Todd–Coxeter coset enumeration process. This book discusses as well the difficulties that arise with multiplication and inverting programs, and of some ways to avoid or overcome them. The final chapter deals with the computational problems related to invariant factors in linear algebra. Mathematicians as well as students of algebra will find this book useful.

Group and Semigroup Rings

1st Edition
Volume 126
September 22, 2011
G. Karpilovsky
English
eBook
9 7 8 0 0 8 0 8 7 2 3 7 7

A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.

Group Theory for Chemists

2nd Edition
December 21, 2010
Kieran C Molloy
English
Paperback
9 7 8 0 8 5 7 0 9 2 4 0 3
eBook
9 7 8 0 8 5 7 0 9 2 4 1 0

The basics of group theory and its applications to themes such as the analysis of vibrational spectra and molecular orbital theory are essential knowledge for the undergraduate student of inorganic chemistry. The second edition of Group Theory for Chemists uses diagrams and problem-solving to help students test and improve their understanding, including a new section on the application of group theory to electronic spectroscopy.Part one covers the essentials of symmetry and group theory, including symmetry, point groups and representations. Part two deals with the application of group theory to vibrational spectroscopy, with chapters covering topics such as reducible representations and techniques of vibrational spectroscopy. In part three, group theory as applied to structure and bonding is considered, with chapters on the fundamentals of molecular orbital theory, octahedral complexes and ferrocene among other topics. Additionally in the second edition, part four focuses on the application of group theory to electronic spectroscopy, covering symmetry and selection rules, terms and configurations and d-d spectra.Drawing on the author’s extensive experience teaching group theory to undergraduates, Group Theory for Chemists provides a focused and comprehensive study of group theory and its applications which is invaluable to the student of chemistry as well as those in related fields seeking an introduction to the topic.

Almost Free Modules

1st Edition
Volume 65
April 29, 2002
P.C. Eklof + 1 more
English
eBook
9 7 8 0 0 8 0 5 2 7 0 5 5

This book provides a comprehensive exposition of the use of set-theoretic methods in abelian group theory, module theory, and homological algebra, including applications to Whitehead's Problem, the structure of Ext and the existence of almost-free modules over non-perfect rings. This second edition is completely revised and udated to include major developments in the decade since the first edition. Among these are applications to cotorsion theories and covers, including a proof of the Flat Cover Conjecture, as well as the use of Shelah's pcf theory to constuct almost free groups. As with the first edition, the book is largely self-contained, and designed to be accessible to both graduate students and researchers in both algebra and logic. They will find there an introduction to powerful techniques which they may find useful in their own work.

Group Representations Volume 1 Part B

1st Edition
Volume 1
July 9, 1992
Gregory Karpilovsky
English
eBook
9 7 8 0 0 8 0 8 7 2 8 6 5

Clifford Theory for Group Representations

1st Edition
Volume 156
May 1, 1989
G. Karpilovsky
English
eBook
9 7 8 0 0 8 0 8 7 2 6 7 4

Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN. (ii) extension from FN. (iii) induction from FN. This is the `Clifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products.The purpose of this monograph is to tie together various threads of the development in order to give a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, i.e. familiarity with basic ring-theoretic, number-theoretic and group-theoretic concepts, and an understanding of elementary properties of modules, tensor products and fields.

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Books in Group theory and generalizations

Group Representations

Group Representations

Semihypergroup Theory

Regular Figures

Computational Problems in Abstract Algebra

Group and Semigroup Rings

Group Theory for Chemists

Almost Free Modules

Group Representations Volume 1 Part B

Clifford Theory for Group Representations