Abstract Algebra: Group Theory for B.A. & B.Sc. Mathematics Students – Complete Guide

Specifically designed for B.A. and B.Sc. students, this textbook serves as a foundational guide to Abstract Algebra. The book is praised for its ability to explain deep and intriguing mathematical concepts in a straightforward manner, making it accessible for undergraduates.

Key Features
Syllabus-Oriented: Covers the entire course of Group Theory as per standard University Unit V guidelines
Rich in Examples: Features numerous solved examples and counter-examples (like the $S_3$ group and Quaternion group) to help students grasp abstract proofs.
Problem-Solving Focus: Includes a large number of fully solved problems from standard textbooks to build student confidence for exams.
Quick Reference: Includes a “Glossary of Main Definitions and Theorems,” which is excellent for last-minute revision.

Table of Contents & Core Topics
The book is systematically divided into four major parts:
1.Groups: Fundamental concepts including Mappings, Binary Compositions, Equivalence Relations, Subgroups, Cyclic Groups, and Lagrange’s Theorem.
2.Homomorphisms and Permutations: Detailed study of Homomorphism, Isomorphism, Cayley’s Theorem, and Permutation Groups.
3.Automorphisms and Conjugate Elements: Advanced topics such as Inner Automorphisms, Conjugate Elements, and the Class Equation of a group.
4.Sylow Theorems & Direct Products: Coverage of p-Groups, Sylow’s Theorems, and Finite Abelian Groups.

The book is highly recommended for students looking for a balance between rigorous theory and practical problem-solving. It concludes with specialized Examination Papers and appendices to ensure students are well-prepared for their university finals.