Group Theory

e-books in Group Theory category

An Elementary Introduction to Group Theory
by M. E. Charkani - AMS , 2018
The theory of groups is a branch of mathematics in which we study the concept of binaryoperations. Group theory has many applications in physics and chemistry, and is potentially applicable in any situation characterized by symmetry.
(7815 views)

Groups Around Us
by Pavel Etingof - Massachusetts Institute of Technology , 2018
These are notes of a mini-course of group theory for high school students. This course covers the most basic parts of group theory with many applications. The notes contain many exercises, which are necessary for understanding the main text.
(5134 views)

An Introduction to the Theory of Groups of Finite Order
by Harold Hilton - Oxford Clarendon Press , 1908
This book aims at introducing the reader to more advanced treatises and original papers on Groups of finite order. The subject requires for its study only an elementary knowledge of Algebra. I have tried to lighten for him the initial difficulties.
(6973 views)

Thin Groups and Superstrong Approximation
by Emmanuel Breuillard, Hee Oh (eds.) - Cambridge University Press , 2014
This book focuses on recent developments concerning various quantitative aspects of thin groups. It provides a broad panorama of a very active field of mathematics at the boundary between geometry, dynamical systems, number theory, and combinatorics.
(6984 views)

Groups and Semigroups: Connections and Contrasts
by John Meakin - University of Nebraska-Lincoln , 2005
In the present paper, I will discuss some of these connections between group theory and semigroup theory, and I will also discuss some rather surprising contrasts between the theories. I will focus primarily on the theory of inverse semigroups.
(10020 views)

Theory and Applications of Finite Groups
by G. A. Miller, H. F. Blichfeldt, L. E. Dickson - J. Wiley , 1916
The book presents in a unified manner the more fundamental aspects of finite groups and their applications, and at the same time preserves the advantage which arises when each branch of an extensive subject is written by a specialist in that branch.
(8561 views)

An Introduction to Group Theory: Applications to Mathematical Music Theory
by Flor Aceff-Sanchez, et al. - BookBoon , 2013
In this text, a modern presentation of the fundamental notions of Group Theory is chosen, where the language of commutative diagrams and universal properties, so necessary in Modern Mathematics, in Physics and Computer Science, is introduced.
(11553 views)

Theory of Groups of Finite Order
by William Burnside - Cambridge University Press , 1897
After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; etc.
(11180 views)

Frobenius Splittings and B-Modules
by Wilberd van der Kallen - Springer , 1993
The course given by the author in 1992 explains the solution by O. Mathieu of some conjectures in the representation theory of arbitrary semisimple algebraic groups. The conjectures concern filtrations of 'standard' representations.
(9478 views)

Congruence Lattices of Finite Algebras
by William DeMeo - arXiv , 2012
We review a number of methods for finding a finite algebra with a given congruence lattice, including searching for intervals in subgroup lattices. We also consider methods for proving that algebras with a given congruence lattice exist...
(9926 views)

Lectures on Topics In The Theory of Infinite Groups
by B.H. Neumann - Tata Institute of Fundamental Research , 1960
As the title suggests, the aim was not a systematic treatment of infinite groups. Instead the author tried to present some of the methods and results that are new and look promising, and that have not yet found their way into the books.
(10391 views)

Lectures on Semi-group Theory and its Application to Cauchy's Problem in Partial Differential Equations
by K. Yosida - Tata Institute of Fundamental Research , 1957
In these lectures, we shall be concerned with the differentiability and the representation of one-parameter semi-groups of bounded linear operators on a Banach space and their applications to the initial value problem for differential equations.
(12776 views)

Finite Group Schemes
by Richard Pink - ETH Zurich , 2005
The aim of the lecture course is the classification of finite commutative group schemes over a perfect field of characteristic p, using the classical approach by contravariant Dieudonne theory. The theory is developed from scratch.
(10552 views)

Galois Groups and Fundamental Groups
by David Meredith - San Francisco State University , 1999
This course brings together two areas of mathematics that each concern symmetry -- symmetry in algebra, in the case of Galois theory; and symmetry in geometry, in the case of fundamental groups. Prerequisites are courses in algebra and analysis.
(11800 views)

Representation Theory of Compact Groups
by Michael Ruzhansky, Ville Turunen - Aalto TKK , 2008
Contents: Groups (Groups without topology, Group actions and representations); Topological groups (Compact groups, Haar measure, Fourier transforms on compact groups..); Linear Lie groups (Exponential map, Lie groups and Lie algebras); Hopf algebras.
(11651 views)

Lectures on Algebraic Groups
by Alexander Kleshchev - University of Oregon , 2005
Contents: General Algebra; Commutative Algebra; Affine and Projective Algebraic Sets; Varieties; Morphisms; Tangent spaces; Complete Varieties; Basic Concepts; Lie algebra of an algebraic group; Quotients; Semisimple and unipotent elements; etc.
(13653 views)

Geometry and Group Theory
by Christopher Pope - Texas A&M University , 2008
Lecture notes on Geometry and Group Theory. In this course, we develop the basic notions of Manifolds and Geometry, with applications in physics, and also we develop the basic notions of the theory of Lie Groups, and their applications in physics.
(20781 views)

Elements of Group Theory
by F. J. Yndurain - arXiv , 2007
The following notes are the basis for a graduate course. They are oriented towards the application of group theory to particle physics, although some of it can be used for general quantum mechanics. They have no pretense of mathematical rigor.
(17081 views)

Interval Groupoids
by W. B. V. Kandasamy, F. Smarandache, M. K. Chetry - arXiv , 2010
This book defines new classes of groupoids, like matrix groupoid, polynomial groupoid, interval groupoid, and polynomial groupoid. This book introduces 77 new definitions substantiated and described by 426 examples and 150 theorems.
(10558 views)

Finite Rank Torsion Free Modules Over Dedekind Domains
by E. Lee Lady - University of Hawaii , 1998
Contents: Modules Over Commutative Rings; Fundamentals; Rank-one Modules and Types; Quasi-Homomorphisms; The t-Socle and t-Radical; Butler Modules; Splitting Rings and Splitting Fields; Torsion Free Rings; Quotient Divisible Modules; etc.
(10179 views)

Lie groups and Lie algebras
by N. Reshetikhin, V. Serganova, R. Borcherds - UC Berkeley , 2006
From the table of contents: Tangent Lie algebras to Lie groups; Simply Connected Lie Groups; Hopf Algebras; PBW Theorem and Deformations; Lie algebra cohomology; Engel's Theorem and Lie's Theorem; Cartan Criterion, Whitehead and Weyl Theorems; etc.
(12641 views)

Why are Braids Orderable?
by Patrick Dehornoy, at al. , 2010
This book is an account of several quite different approaches to Artin's braid groups, involving self-distributive algebra, uniform finite trees, combinatorial group theory, mapping class groups, laminations, and hyperbolic geometry.
(13253 views)

Introduction to Lie Groups and Lie Algebras
by Alexander Kirillov, Jr. - SUNY at Stony Brook , 2010
The book covers the basic contemporary theory of Lie groups and Lie algebras. This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. Written in an informal style.
(14953 views)

Algebraic Groups, Lie Groups, and their Arithmetic Subgroups
by J. S. Milne , 2010
This work is a modern exposition of the theory of algebraic group schemes, Lie groups, and their arithmetic subgroups. Algebraic groups are groups defined by polynomials. Those in this book can all be realized as groups of matrices.
(13063 views)

Introduction to Arithmetic Groups
by Dave Witte Morris - arXiv , 2015
This revised version of a book in progress on arithmetic groups and locally symmetric spaces contains several additional chapters, including the proofs of three major theorems of G. A. Margulis (superrigidity, arithmeticity, and normal subgroups).
(11181 views)

Smarandache Semigroups
by W. B. Vasantha Kandasamy - American Research Press , 2002
The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties for reference.
(11032 views)

Groupoids and Smarandache Groupoids
by W. B. Vasantha Kandasamy - American Research Press , 2002
This book by Dr. W. B. Vasantha aims to give a systematic development of the basic non-associative algebraic structures viz. Smarandache groupoids. Smarandache groupoids exhibits simultaneously the properties of a semigroup and a groupoid.
(11814 views)

Group Theory
by J. S. Milne , 2009
Contents: Basic Definitions and Results; Free Groups and Presentations; Coxeter Groups; Automorphisms and Extensions; Groups Acting on Sets; The Sylow Theorems; Subnormal Series; Solvable and Nilpotent Groups; Representations of Finite Groups.
(14562 views)

Groups as Graphs
by W. B. V. Kandasamy, F. Smarandache - CuArt , 2009
In this book, for the first time, the authors represented every finite group in the form of a graph. This study is significant because properties of groups can be immediately obtained by looking at the graphs of the groups.
(13339 views)

Galois Groups and Fundamental Groups
by Leila Schneps - Cambridge University Press , 2003
This book contains eight articles which focus on presenting recently developed new aspects of the theory of Galois groups and fundamental groups, avoiding classical aspects which have already been developed at length in the standard literature.
(14240 views)

Group theory for Maths, Physics and Chemistry
by Arjeh Cohen, Rosane Ushirobira, Jan Draisma , 2007
Symmetry plays an important role in chemistry and physics. Group captures the symmetry in a very efficient manner. We focus on abstract group theory, deal with representations of groups, and deal with some applications in chemistry and physics.
(14872 views)

Group Theory
by Ferdi Aryasetiawan - University of Lund , 1997
The text deals with basic Group Theory and its applications. Contents: Abstract Group Theory; Theory of Group Representations; Group Theory in Quantum Mechanics; Lie Groups; Atomic Physics; The Group SU2: Isospin; The Point Groups; The Group SU3.
(16884 views)

Symmetry Groups and Their Applications
by Willard Miller - Academic Press , 1972
A beginning graduate level book on applied group theory. Only those aspects of group theory are treated which are useful in the physical sciences, but the mathematical apparatus underlying the applications is presented with a high degree of rigor.
(16625 views)

An Elementary Introduction to Groups and Representations
by Brian C. Hall - arXiv , 2000
An elementary introduction to Lie groups, Lie algebras, and their representations. Topics include definitions and examples of Lie groups and Lie algebras, the basics of representations theory, the Baker-Campbell-Hausdorff formula, and more.
(19787 views)

Notes on Categories and Groupoids
by P. J. Higgins - Van Nostrand Reinhold , 1971
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(16218 views)

Combinatorial Group Theory
by Charles F. Miller III - University of Melbourne , 2004
Lecture notes for the subject Combinatorial Group Theory at the University of Melbourne. Contents: About groups; Free groups and presentations; Construction of new groups; Properties, embeddings and examples; Subgroup Theory; Decision Problems.
(15845 views)

Group Characters, Symmetric Functions, and the Hecke Algebra
by David M. Goldschmidt - American Mathematical Society , 1993
The book covers a set of interrelated topics, presenting a self-contained exposition of the algebra behind the Jones polynomial along with various excursions into related areas. Directed at graduate students and mathematicians.
(12462 views)

Introduction to Groups, Invariants and Particles
by Frank W. K. Firk - Orange Grove Texts Plus , 2000
This is an introduction to group theory, with an emphasis on Lie groups and their application to the study of symmetries of the fundamental constituents of matter. The text was written for seniors and advanced juniors, majoring in the physical sciences.
(20214 views)

Group Theory: Birdtracks, Lie's, and Exceptional Groups
by Predrag Cvitanovic - Princeton University Press , 2011
A book on the theory of Lie groups for researchers and graduate students in theoretical physics and mathematics. It answers what Lie groups preserve trilinear, quadrilinear, and higher order invariants. Written in a lively and personable style.
(16431 views)