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Finite groups
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Daniel Gorenstein
This text examines finite groups.
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Finite Group Theory
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by
M Aschbacher
During the last 30 years the theory of finite groups has developed dramatically. Our understanding of finite simple groups has been enhanced by their classification. Many questions about arbitrary groups can be reduced to similar questions about simple groups and applications of the theory are beginning to appear in other branches of mathematics. ...
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3-Transposition Groups
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Michael Aschbacher
In 1970 Bernd Fischer proved his beautiful theorem classifying the almost simple groups generated by 3-transpositions, and in the process discovered three new sporadic groups, now known as the Fischer groups. Since then, the theory of 3-transposition groups has become an important part of finite simple group theory, but Fischer's work has remained ...
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Finite Reductive Groups, Related Structures and Representations
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Marc Cabanes (Editor)
This volume focuses on the representation theory of groups and related structures, combining the modular representation theory of finite groups of Richard Brauer and the representation theory of reductive groups of George Lusztig.
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Classes of Finite Groups.
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by
Adolfo Ballester-Bolinches
Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered ...
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Representation theory of finite groups and associative algebras
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by
Charles W Curtis
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Linear Representations of Finite Groups
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by
Jean-Pierre Serre
This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. This is a fundamental result of constant use in mathematics as well as in quantum chemistry or physics. The examples ...
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Theory of Finite Groups
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by
Hans Kurzweil, Bernd Stellmacher
From reviews of the German edition: 'This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions. One who completes ...
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Introduction to the theory of finite groups.
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by
Walter Ledermann
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Enumeration of Finite Groups
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by
Simon R Blackburn, Peter M Neumann, Geetha Venkataraman
How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of ...
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Profinite Groups, Arithmetic, and Geometry
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by
Stephen S. Shatz
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Whitehead groups of finite groups
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by
Oliver
This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of ...
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Rotations, Quaternions, and Double Groups
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by
Simon L Altmann
Quaternions are a simple and powerful tool for handling rotations and double groups. This book gives a complete treatment of finite point groups as subgroups of the full rotation group and emphasizes geometrical and topological methods which permit a unique definition of the quaternion parameters for all operations of such groups. An important ...
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Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups
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John Horton Conway (Photographer)
This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections
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A Course in Group Theory
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by
John Humphreys, MRC
This book is an excellent and self-contained introduction to the theory of groups, covering all topics likely to be encountered in undergraduate courses. In recent years there has been a great deal of research in group theory and a large number of books have been published. However, most of these are aimed at the postgraduate market and a good ...
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Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains
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by
Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
Line up a deck of 52 cards on a table. Randomly choose two cards and switch them. How many switches are needed in order to mix up the deck? Starting from a few concrete problems such as random walks on the discrete circle and the finite ultrametric space this book develops the necessary tools for the asymptotic analysis of these processes. This ...
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Fourier Analysis on Finite Groups and Applications
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by
Audrey Terras
This book gives a friendly introduction to Fourier analysis on finite groups, both commutative and non-commutative. Aimed at students in mathematics, engineering and the physical sciences, it examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research. With applications in chemistry, ...
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Groups, Representations and Physics
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by
H F Jones
Illustrating the fascinating interplay between physics and mathematics, "Groups, Representations and Physics, Second Edition" provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the ...
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The Structure of Groups of Prime Power Order
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by
C R Leedham-Green, S McKay
The coclass project (1980-1994) provided a new and powerful way to classify finite p-groups. This monograph gives a coherent account of the thinking from which the philosophy that lead to this classification developed. The authors provide a careful summary and explanation of the many and difficult original research papers on the coclass conjecture ...
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Sphere Packings, Lattices, and Groups
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by
John Horton Conway
The third edition of this timely, definitive, and popular book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space? The authors also continue to examine related problems such as the kissing number problem, the covering problem, the quantizing problem, and the ...
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Representation Theory of Finite Groups and Finite-Dimensional Algebras
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G Michler, Ringel
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Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras
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by
Meinolf Geck, Gotz Pfeiffer
Finite Coxeter groups and related structures arise naturally in several branches of mathematics, for example, the theory of Lie algebras and algebraic groups. The corresponding Iwahori-Hecke algebras are obtained by a certain deformation process. They have applications in the representation theory of groups of Lie type and the theory of knots and ...
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Skew Linear Groups
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by
Shirvani, Wehrfritz
This book is concerned with subgroups of groups of the form GL(n,D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the ...
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Characters of Reductive Groups Over a Finite Field
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George Lusztig
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Handbook of Tilting Theory
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by
Lidia Angeleri Hugel (Editor), Dieter Happel (Editor), Henning Krause (Editor)
Tilting theory originates in the representation theory of finite dimensional algebras. Today the subject is of much interest in various areas of mathematics, such as finite and algebraic group theory, commutative and non-commutative algebraic geometry, and algebraic topology. The aim of this book is to present the basic concepts of tilting theory ...
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