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Contemporary Abstract Algebra
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ISBN
:
9788173192692
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Publisher
:
Narosa Publishing House
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Subject
:
Encyclopaedias & Reference Works
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Binding
:
Paperback
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Pages
:
581
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Year
:
1999
₹
450.0
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378.0
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Description
This is the first volume of the book Algebra planned by the authors to provide adequate preparation in algebra to prospective teachers and researchers in mathematics and related areas. Beginning with groups of symmetries of plane configurations. It studies groups (with operators) and their homomorphisms, presentations of groups by generators and relations , direct and semidirect products, Sylow's theorems, soluble, nilpotent and Abelian groups. The volume ends with Jordan's classification of finite subgroups of the group of orthogonal transformations of R'. An attractive feature of the book is its richness in purposeful examples and instructive exercise with a focus on the roots of algebra in number theory, geometry and theory of equations. Table of Contents Perface Part 1 Integers and Equivalence Relations Chapter: Preliminaries Part 2 Groups Chapter 1 Introduction to Groups Chapter 2 Groups Chapter 3 Finite Groups; Subgroups Chapter 4 Cyclic Groups Chapter 5 Permutation Groups Chapter 6 Isomorphisms Chapter 7 Cosets and Lagrange's Theorem Chapter 8 External Direct Products Chapter 9 Normal Subgroups and Factor Groups Chapter 10 Group Homomorphisms Chapter 11 Fundamental Theorem of Finite Abelian Part 3 Rings Chapter 12 Introduction to Rings Chapter 13 Integral Domains Chapter 14 Ideals and Factor Rings Chapter 15 Ring Homomorphisms Chapter 16 Polynomial Rings Chapter 17 Factorization of Polynomials Chapter 18 Divisibility in Integral Domains Part 4 Fields Chapter 19 Vector Spaces Chapter 20 Extension Fields Chapter 21 Algebraic Extensions Chapter 22 Finite Fields Chapter 23 Geometric Constructions Part 5 Special Topics Chapter 24 Sylow Theorems Chapter 25 Finite Simple Groups Chapter 26 Generators and Relations Chapter 27 Symmetry Groups Chapter 28 Frieze Groups and Crystallographic Groups Chapter 29 Symmetry and Counting Chapter 30 Cayley Digraphs of Groups Chapter 31 Introduction to Algebraic Coding Theory Chapter 32 An Introduction to Galois Theory Chapter 33 Cyclotomic Extensions Selected Answers Text Credits Photo Credits Notations Index of Mathematicians Index of Terms
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