## see also

**Lie Groups** (18)

## e-books in Group Theory category

**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.

(

**297**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.

(

**1993**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.

(

**2088**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.

(

**5011**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.

(

**3785**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.

(

**6112**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.

(

**5771**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.

(

**4852**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...

(

**4917**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.

(

**5293**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.

(

**7357**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.

(

**5554**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.

(

**6180**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.

(

**6652**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.

(

**7282**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.

(

**13011**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.

(

**10938**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.

(

**5471**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.

(

**5191**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.

(

**7492**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.

(

**7819**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.

(

**9627**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.

(

**7707**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).

(

**6305**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.

(

**5763**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.

(

**5998**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.

(

**8548**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.

(

**7409**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.

(

**8884**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.

(

**9438**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.

(

**9769**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.

(

**9686**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.

(

**13298**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.

(

**10047**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.

(

**9549**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.

(

**7398**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.

(

**13878**views)

**Group Theory: Birdtracks, Lie's, and Exceptional Groups**

by

**Predrag Cvitanovic**-

**Princeton University Press**,

**2008**

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.

(

**10290**views)