Graduate Text in Mathematics by Derek J. S. Robinson is a comprehensive resource for students and professionals looking to expand their knowledge of mathematics. This comprehensive textbook covers a wide range of mathematical topics, making it an ideal resource for graduate students, researchers, and professionals in the field.
The book covers a wide range of mathematical concepts, from algebra and topology to complex analysis and differential equations. Each chapter is written in a clear and concise manner and is accompanied by numerous examples and exercises to help reinforce the material. This makes Graduate Text in Mathematics an ideal resource for students looking to deepen their understanding of mathematical concepts and techniques.
One of the key strengths of Graduate Text in Mathematics is its focus on the underlying theory and concepts. The author presents the material in a way that is both accessible and rigorous, making it ideal for students who are looking to develop a strong foundation in mathematics. The book also provides a solid foundation for students who wish to pursue further study in related fields, such as mathematical physics or applied mathematics.
Table of Contents
Chapter 1 Fundamental Concepts of Group Theory
- Binary Operations, Semigroups, and Groups
- Examples of Groups
- Subgroups and Cosets
- Homomorphisms and Quotient Groups
- Endomorphisms and Quotient Groups
- Permutation Groups and Group Actions
CHAPTER 2 Free Groups and Presentations
- Free Groups
- Presentations of Groups
- Varieties of Groups
CHAPTER 3 Decompositions of a Group
- Series and Composition Series
- Some Simple Groups
- Direct Decompositions
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CHAPTER 4 Abelian Groups
- Torsion Groups and Divisible Groups
- Direct Sums of Cyclic and Quasicyclic Groups
- Pure Subgroups and p-Groups
- Torsion-Free Groups
CHAPTER 5 Soluble and Nilpotent Groups
- Abelian and Central Series
- Nilpotent Groups
- Groups of Prime-Power Order
- Soluble Groups
CHAPTER 6 Free Groups and Free Products
- Further Properties of Free Groups
- Free Products of Groups
- Subgroups of Free Products
- Generalized Free Products
CHAPTER 7 Finite Permutation Groups
- Multiple Transitivity
- Primitive Permutation Groups
- Classification of Sharply /c-Transitive Permutation Groups
- The Mathieu Groups
CHAPTER 8 Representations of Groups
- Representations and Modules
- Structure of the Group Algebra
- Characters
- Tensor Products and Representations
- Applications to Finite Groups
CHAPTER 9 Finite Soluble Groups
- Hall 7r-Subgroups
- Sylow Systems and System Normalizers
- p-Soluble Groups
- Supersoluble Groups
- Formations
CHAPTER 10 The Transfer and Its Applications
- The Transfer Homomorphism
- Gain’s Theorems
- Frobenius’s Criterion for p-Nilpotence
- Thompson’s Criterion for p-Nilpotence
- Fixed-Point-Free Automorphisms
CHAPTER 11 The Theory of Group Extensions
- Group Extensions and Covering Groups
- Homology Groups and Cohomology Groups
- The Gruenberg Resolution
- Group-Theoretic Interpretations of the (Co)homology Groups
CHAPTER 12 Generalizations of Nilpotent and Soluble Groups
- Locally Nilpotent Groups
- Some Special Types of Locally Nilpotent Groups
- Engel Elements and Engel Groups
- Classes of Groups Defined by General Series
- Locally Soluble Groups
CHAPTER 13 Subnormal Subgroups
- Joins and Intersections of Subnormal Subgroups
- Permutability and Subnormality
- The Minimal Condition on Subnormal Subgroups
- Groups in Which Normality Is a Transitive Relation
- Automorphism Towers and Complete Groups
CHAPTER 14 Finiteness Properties
- Finitely Generated Groups and Finitely Presented Groups
- Torsion Groups and the Burnside Problems
- Locally Finite Groups
- 2-Groups with the Maximal or Minimal Condition
- Finiteness Properties of Conjugates and Commutators
CHAPTER 15 Infinite Soluble Groups
- Soluble Linear Groups
- Soluble Groups with Finiteness Conditions on Abelian Subgroups
- Finitely Generated Soluble Groups and the Maximal Condition on Normal Subgroups
- Finitely Generated Soluble Groups and Residual Finiteness
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In addition to its comprehensive coverage of mathematical concepts, Graduate Text in Mathematics also includes a wealth of supplementary material that is designed to help students better understand and retain the material. This includes appendices on mathematical notation and symbols, as well as numerous examples and exercises that are designed to reinforce the concepts presented in each chapter.
For students looking to access the book’s material electronically, Graduate Text in Mathematics is available in PDF format for download. This makes it easy for students to access the book from anywhere, at any time, and on a variety of devices. The PDF format also provides the added convenience of being searchable and easily navigable, making it easier for students to find the information they need quickly and efficiently.
In conclusion, Graduate Text in Mathematics by Derek J. S. Robinson is an excellent resource for anyone looking to expand their knowledge of mathematics. Whether you are a graduate student just starting out in the field or a professional looking to brush up on your knowledge, this book provides a clear, comprehensive, and accessible guide to the subject. With its focus on the underlying theory and concepts and its wealth of supplementary material, this book is sure to be a valuable resource for years to come.
