Topics covered:
Week 1: Groups, subgroups, homomorphisms, normal subgroups, quotient groups, direct products, isomorphism theorems.Week 2: Composition series, Jordan-Holder theorem, solvable groups, nilpotent groups. Some examples.
Week 3-4: Simplicity of PSL(n,k). Groups acting on sets. Class equation. Sylow theory.
Week 5: Semi-direct products of groups. Examples. Wreath products. Sylow subgroups of the symmetric group.
Week 6: Categorical notions. Functors. Representable functors. Universal objects. Product, co-product, fiber product. Projective and inductive limits.
Assignments:
Assignment 1 (due Mon, Sept 10).Solutions to Assignment 1.Assignment 2 (due Mon, Sept 24). Solutions to Assignment 2.
Assignment 3 (due Wed, Oct 10). Solutions to Assignment 3.
Assignment 4 (due Mon, Nov 5). Solutions to Assignment 4.
Assignment 5 (due Mon, Nov 19). Solutions to Assignment 5.
Assignment 6 (due Wed, Dec 5). Saugata Basu