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This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The contents focus on the properties of groups, subgroups, cyclic groups, permutation groups, cosets and Lagrange's theorem, normal subgroups and factor groups, group homomorphisms and isomorphisms, automorphisms, direct products, group actions and Sylow theorems. Pedagogical elements such as end of chapter exercises and solved problems are included to help understand abstract notions. Intermediate lemmas are also carefully designed so that they not only serve the theorems but are also valuable independently. The book is a useful reference to undergraduate and graduate students besides academics.
List of contents
Group.- Finite Groups and Subgroups.- Cyclic Groups.- Permutation Groups.- Cosets and Lagrange's Theorem.- Normal Subgroups and Factor Groups.- Group Homomorphism and Isomorphism.- Automorphisms.- Direct Products.- Group Actions.- Sylow Theorems.
About the author
Dinesh Khattar, Ph.D., is a professor in the Department of Mathematics, Kirori Mal College, University of Delhi, India. He also served as the Principal of Kirori Mal College from 2015 to 2018. He is a topper (Gold Medalist) in his B.Sc. and M.Sc. exams. He received Dr. S. Radhakrishnan Memorial National Teachers Award 2015 for the contribution in the field of education. He has also been awarded prestigious Commonwealth Scholarship for pursuing research in UK. He is actively involved in research and presented papers in prestigious international conferences across several countries. Dr. Khattar has been a member of curriculum development committee for B.Sc. and M.Sc. programs in various universities including University of Delhi. He is also an author of many books on mathematics.
Neha Agrawal has completed her graduation and post-graduation degrees from Kirori Mal College, University of Delhi, India. She has done her M.Phil. and Ph.D. from University of Delhi. Her area of interest is nonlinear dynamical systems and chaos theory. She has been working as an assistant professor in the Department of Mathematics, Kirori Mal College since 2012. She has teaching experience of 12 years. She has published number of research papers in international journals.
