Topics in Abstract Algebra

Contents: Preface to the Fourth Edition. Preface to the First Edition. 1. Preliminaries. 2. Integers. 3. Groups. 4. Permutation groups. 5. Subgroups. 6. Homomorphisms of groups. 7. Direct product of groups. 8. Symmetry. 9. Finite Abelian groups.10. Sylow theorems.11. Simple groups.12. Rings.13. Ideals and homomorphisms of rings.14. Factorization in integer domains.15. Polynomial rings. Appendices. Bibliography. Index. Replete with thought-provoking examples and worked-out exercises, this third edition of Topics in Abstract Algebra is designed in accordance with the new Choice Based Credit System (CBCS) syllabus of Abstract Algebra and Advanced Abstract Algebra prescribed by UGC for all Indian universities at the UG Honours/Advanced level. Students appearing for competitive entrance examinations such as NET, JAM, ISI, IISc., TIFR, NBHM, GATE, SET or MCA will benefit immensely from the carefully selected Solved Problems, about a hundred of which (of MCQ type) have been newly added to the present edition. Interesting insights to the history of mathematics and mathematicians are also provided in the course of discussion to enable the readers understand the concepts in the right perspective.…