Group Theory As Per the University of Delhi B.Sc. Mathematics (Hons) Syllabi for Algebra II (Sem-3) and Algebra V (Sem-6)

Description Designed as a text for undergraduate students of mathematics,this book meets the curriculum requirements of the University ofDelhi. It specifically caters to the syllabus of Group Theorycovered in Algebra II (Semester 3) and Algebra V (Semester 6) andfollows an easy-paced treatment of the basic concepts. Learning objectives at the beginning of each chapter Concepts illustrated with 550 solved examples Stepwise proofs of 200 theorems Chapter-wise summary for ready reference Graded exercises Concepts reinforced by true/false questions Answers/hints to all the 540 unsolved problems 1. Definition and Examples of Groups 2. Properties and Characterizations of Groups 3. Subgroups 4. Cyclic Groups 5. Dihedral and Quarternion Groups 6. Permutation Groups I 7. External Direct Products 8. Isomorphisms 9. Lagrange's Theorem 10. Normal Subgroups 11. Factor Groups 12. Homomorphisms 13. Automorphisms 14. Centralizer Normalizer and Centre 15. Direct Products 16. Fundamental Theorem of Finite Abelian Groups 17. Group Action 18. Permutation Representation of a Group 19. Generalized Cayley's Theorem 20. Conjugacy and Class Equation 21. Permutation Groups II 22. Sylow's Theorems and Non-Simplicity Tests 23. Composition Series 24. Solvable Groups Dr Sudesh Kumari Shah is Associate Professor atthe Department of Mathematics, Sri Venkateswara College, Universityof Delhi. An alumnus of IIT Delhi, she has been teachingundergraduate and postgraduate students of the University of Delhifor more than 30 years. Dr Asha Gauri Shankar is Associate Professor atthe Department of Mathematics, Lakshmibai College, University ofDelhi. She obtained a Ph.D. from Imperial College London. She wasawarded ';Teacher of Excellence' in 2009 by the University ofDelhi. The award was conferred by Dr A. P. J. Abdul Kalam.