Abelian group, Symmetric group, Definitions and Examples – Basic properties
Subgroups – Cyclic subgroup - Index of a group – Order of an element – Fermat theorem – A Counting Principle - Normal Subgroups and Quotient Groups.
Homomorphism – Cauchy‘s theorem for Abelian groups –Automorphisms – Inner automorphism - Cayley‘s theorem, permutation groups.
Definition and Examples –Some Special Classes of Rings – Commutative ring – Field –Integral domain - Homomorphisms of Rings.
Ideals and Quotient Rings – More Ideals and Quotient Rings – Maximal ideal - The field of Quotients of an Integral Domain.
Reference Book:
1. Modern Algebra by Surjeet Singh and QaziZameeruddin, Vikas Publishing house, 1992. 2. Modern Algebra by A.R.Vasishtha, Krishna PrakashanMandir, Meerut, 1994 - 95.
Text Book:
Topics in Algebra by I.N. Herstein, John Wiley & Sons, New York, 2007. Unit I: Chapter 2: Sections: 2.1-2.3. Unit II: Chapter 2: Sections: 2.4-2.6. Unit III: Chapter 2: Sections: 2.7-2.10. Unit IV: Chapter 3: Sections: 3.1-3.3. Unit V: Chapter 3: Sections: 3.4-3.6.