General

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...

Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Groebner bases, whilst taking in all the usual material of a traditional introductory course. In addition there is a rich supply of topics like cryptography, factoring...

The aim of this book is to present a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. The author starts by discussing the...

This book, first published in 2000, focuses on homological aspects of equivariant modules. It presents a homological approximation theory in the category of equivariant modules, unifying the Cohen-Macaulay approximations in commutative ring theory and...

This two-volume book contains selected papers from the international conference 'Groups St Andrews 1997 in Bath'. The articles cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together...

This two-volume book contains selected papers from the international conference 'Groups St Andrews 1997 in Bath'. The articles cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together...

The representation theory of reductive algebraic groups and related finite reductive groups is a subject of great topical interest and has many applications. The articles in this volume provide introductions to various aspects of the subject, including...

Galois theory is a central part of algebra, dealing with symmetries between solutions of algebraic equations in one variable. This is a collection of papers from the participants of a conference on Galois theory, and brings together articles from some of...

This book is an introduction to the contemporary representation theory of Artin algebras, by three very distinguished practitioners in the field. Beyond assuming some first-year graduate algebra and basic homological algebra, the presentation is entirely...

This book provides a detailed but concise account of the theory of structure of finite p-groups admitting p-automorphisms with few fixed points. The relevant preliminary material on Lie rings is introduced and the main theorems of the book on the...

This book surveys progress in the domains described in the hitherto unpublished manuscript 'Esquisse d'un Programme' (Sketch of a Program) by Alexander Grothendieck. It will be of wide interest amongst workers in algebraic geometry, number theory,...

This volume contains original research articles by many of the world's leading researchers in algebraic and Lie groups. Its inclination is algebraic and geometric, although analytical aspects are included. The central theme reflects the interests of R. W...

This book presents a complete classification of the transitive permutation representations of rank at most five of the sporadic simple groups and their automorphism groups, together with a comprehensive study of the vertex-transitive graphs associated...

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of...

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations...

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the...

In the summer semester of 1897 David Hilbert (1862-1943) gave an introductory course in Invariant Theory at the University of Gottingen. This book is an English translation of the handwritten notes taken from this course by Hilbert's student Sophus...

This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions,...

This two-volume book contains selected papers from the international conference 'Groups 1993 Galway/St Andrews' which was held at University College, Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes...

This two-volume book contains selected papers from the international conference 'Groups 1993 Galway/St Andrews' which was held at University College Galway in August 1993. The wealth and diversity of group theory is represented in these two volumes. Five...

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text,...

Many of the ideas introduced by Macaulay in this book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring', however, it is less...

In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on...

The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links,...

In this book Professor Rees introduces and proves some of the main results of the asymptotic theory of ideals. The author's aim is to prove his Valuation Theorem, Strong Valuation Theorem, and Degree Formula, and to develop their consequences. The last...

These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of...

In 1977 several eminent mathematicians were invited to Durham to present papers at a short conference on homological and combinatorial techniques in group theory. The lectures, published here, aimed at presenting in a unified way new developments in the...

Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author...

In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on...

This volume provides a clear and self-contained introduction to important results in the theory of rings and modules. Assuming only the mathematical background provided by a normal undergraduate curriculum, the theory is derived by comparatively direct...

Degree students of mathematics are often daunted by the mass of definitions and theorems with which they must familiarize themselves. In the fields algebra and analysis this burden will now be reduced because in A Handbook of Terms they will find...

This volume contains selected papers by leading researchers from the international conference entitled Tits Buildings and the Model Theory of Groups, held in Wurzburg in 2000. The first part of the book provides a general introduction to many aspects of...

Representation theory and character theory have proved essential in the study of finite simple groups since their early development by Frobenius. The author begins by presenting the foundations of character theory in a style accessible to advanced...

Non-commutative fields (also called skew fields or division rings) have not been studied as thoroughly as their commutative counterparts, and most accounts have hitherto been confined to division algebras - that is skew fields finite dimensional over...

Sporadic Groups is the first step in a programme to provide a uniform, self-contained treatment of the foundational material on the sporadic finite simple groups. The classification of the finite simple groups is one of the premier achievements of modern...

Professor Sawyer's book is based on a course given to the majority of engineering students in their first year at Toronto University. Its aim is to present the important ideas in linear algebra to students of average ability whose principal interests lie...

Presenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This book presents...

Poincare duality algebras originated in the work of topologists on the cohomology of closed manifolds, and Macaulay's dual systems in the study of irreducible ideals in polynomial algebras. These two ideas are tied together using basic commutative...

In recent years there has developed a satisfactory and coherent theory of orthogonal polynomials in several variables, attached to root systems, and depending on two or more parameters. These polynomials include as special cases: symmetric functions;...

A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all four combinations are equivalent). The study of these rings grew out of the theory of representations of a finite group as a group of matrices over a...