Groups and group theory

In the second part of the 20th century, algebraic methods have emerged as a powerful tool to study theories of physical phenomena, especially those of quantal systems.

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory.

The present text is an introduction to the theory of association schemes.

The theory of groups and Lie algebras is interesting for many reasons.

This book is a carefully written exposition of Coxeter groups, an area of mathematics which appears in algebra, geometry, and combinatorics.

Let FG be the group ring of a group G over a field F.

Polycyclic groups are built from cyclic groups in a specific way.

A Course on Finite Groups introduces the fundamentals of group theory to advanced undergraduate and beginning graduate students.

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This book is based on notes for a master's course given at Queen Mary, University of London, in the 1998/9 session.

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications.

Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques.

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry.

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brun Workshop in Galway, Ireland in April 2011.

Learning and Generalization provides a formal mathematical theory addressing intuitive questions of the type: How does a machine learn a concept on the basis of examples?

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common.

The most important invariant of a topological space is its fundamental group.

We very much hope that this book will be read by the interested student (and not just be parked on a shelf for occasional consultation).

Aimed at advanced undergraduate and beginning graduate students, this book provides a first taste of the theory of Lie groups as an appetiser for a more substantial further course.

The aim of this book is the classification of symplectic amalgams - structures which are intimately related to the finite simple groups.

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This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation.

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "e;Lie Theory and Its Applications in Physics"e; held in Sofia (Bulgaria) in June 2023.

This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms "e;up to uniformly bounded error"e;.

This book provides a complete and comprehensive classification of normal 2-coverings of non-abelian simple groups and their generalizations.

The theory of table algebras was introduced in 1991 by Z.

The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics.

Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology.

Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration.