Abstract Algebra: An Interactive Approach
Understanding the Group Concept Introduction to Groups Modular Arithmetic Prime Factorizations The Definition of a Group The Structure within a Group Generators of Groups Defining Finite Groups in Mathematica and GAP Subgroups Patterns within the Cosets of Groups Left and Right Cosets How to Write a Secret Message Normal Subgroups Quotient Groups Mappings between Groups Isomorphisms Homomorphisms The Three Isomorphism Theorems Permutation Groups Symmetric Groups Cycles Cayley's Theorem Numberin…
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- Full title :Abstract Algebra : An Interactive Approach.
Summary
Understanding the Group Concept Introduction to Groups Modular Arithmetic Prime Factorizations The Definition of a Group The Structure within a Group Generators of Groups Defining Finite Groups in Mathematica and GAP Subgroups Patterns within the Cosets of Groups Left and Right Cosets How to Write a Secret Message Normal Subgroups Quotient Groups Mappings between Groups Isomorphisms Homomorphisms The Three Isomorphism Theorems Permutation Groups Symmetric Groups Cycles Cayley's Theorem Numbering the PermutationsBuilding Larger Groups from Smaller Groups The Direct Product The Fundamental Theorem of Finite Abelian Groups Automorphisms Semi-Direct Products The Search for Normal Subgroups The Center of a Group The Normalizer and Normal Closure Subgroups Conjugacy Classes and Simple Groups The Class Equation and Sylow's Theorems Solvable and Insoluble Groups Subnormal Series and the Jordan-Hölder Theorem Derived Group Series Polycyclic Groups Solving the Pyraminx Introduction to Rings Groups with an Additional Operation The Definition of a Ring Entering Finite Rings into GAP and Mathematica Some Properties of Rings The Structure within Rings Subrings Quotient Rings and Ideals Ring Isomorphisms Homomorphisms and Kernels Integral Domains and Fields Polynomial Rings The Field of Quotients Complex Numbers Ordered Commutative RingsUnique FactorizationFactorization of Polynomials Unique Factorization Domains Principal Ideal Domains Euclidean Domains Finite Division Rings Entering Finite Fields in Mathematica or GAP Properties of Finite Fields Cyclotomic Polynomials Finite Skew Fields The Theory of Fields Vector Spaces Extension Fields Splitting Fields Galois Theory The Galois Group of an Extension Field The Galois Group of a Polynomial in Q The Fundamental Theorem of Galois Theory Solutions of Polynomial Equations Using Radicals Bibliography Answers to.
Odd Problems IndexProblems appear at the end of each chapter.
Edition Statements
- Publication Date:©2011.
Publication Statements
- Publisher(s):CRC Press
- Place of Publication:Bosa Roca
- Language:eng
- Publication Date:©2011.
The Physical Object
- Description:1 online resource (550 pages).
Edition Identifiers
- ISBN:9781420094534, 142009453X
- oclc:on1058334659
- LC Classification:QA162 ǂb .P385 2010eb
Table of Contents
Front cover -- Contents -- List of Figures -- List of Tables -- Preface -- Acknowledgments -- About the Author -- Symbol Description -- Mathematica® vs. GAP -- Chapter 1. Understanding the Group Concept -- Chapter 2. The Structure within a Group -- Chapter 3. Patterns within the Cosets of Groups -- Chapter 4. Mappings between Groups -- Chapter 5. Permutation Groups -- Chapter 6. Building Larger Groups from Smaller Groups -- Chapter 7. The Search for Normal Subgroups -- Chapter 8. Solvable and Insoluble Groups -- Chapter 9. Introduction to Rings -- Chapter 10. The Structure within Rings -- Chapter 11. Integral Domains and Fields -- Chapter 12. Unique Factorization -- Chapter 13. Finite Division Rings -- Chapter 14. The Theory of Fields -- Chapter 15. Galois Theory -- Answers to Odd-Numbered Problems -- Back cover.
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