Definition of Groups, Basic Examples of Groups including Symmetric Groups, Subgroups. Cyclic Groups and Factor Groups, Lagrange’s Theorem. Normal Subgroups. Quotient Groups.

Homomorphisms, Kernal of a homomorphism, Automorphisms, Cauchy’s Theorem and Sylow’s Theorem for Abelian Groups, Cayley’s Theorem.

Permutation Groups, Conjugate Elements, Normalizer of an Element, Index of Normalizer, Center of a Group, Cauchy’s Theorem on Prime Order, the Number of Conjugate Classes ��(��) for a Permutation Group, Counting Principles, Cauchy Theorem.

1.  M.Artin, ‘Algebra’, Prentice Hall inc., 1994.
2. I. N. Herstein, ‘Topics in Algebra’, Second Edition, John Wiley and Sons, 2000.
3. Joseph A. Gallian, ‘Contemporary Abstract Algebra’, Cengage Learning, 2013.
4. John B. Fraleigh, ‘A First Course in Abstract Algebra’, Narosa Publishing House, 2003.