571 Graduate Algebra II, 2010
Course Page

Classes: MW 10:35-11:55, Burn 920. 
There will be classes on Feb 16, 17:00-18:30, March 16, 17:00-18:30 and March 5,  10:30-13:30
instead of  March 8,10 and April 12, 14.


OFFICE HOURS BEFORE THE EXAM April 18 (Sunday), 19:00-21:00 and  April 19,  12:30-13:30 


Course Outline

Schedule:

Jan 4-8 Groups, subgroups, homomorphisms, 3 isomorphism theorems.
Group Actions on Sets, Sylow theorems. Notes1

Assignment 1. Due Jan 25
Problems 1-6 from pages 10-11 (Notes) and 1-7 from page 13(notes)

Solutions to assignment 1

Jan 18- Free groups, Notes2

Jan 27-Feb 8 Nilpotent and Solvable groups, Notes3
*******************
Assignment 2. Due Feb 15
1. Prove that the commutator subgroup of a free group of rank >1 is not finitely generated (Hint:  Construct  a Schreier graph for  H=F', where F=F(a,b)
a free group  of rank 2)

2. Problems from  Notes3:
Section 1.5 #7,
All Problems for Section 1.7
Section 1.8 Problems 4-9

3. Prove that a finitely generated nilpotent group has a normal torsion free subgroup of finite index.
*******************
Oxford course on abelian, nilpotent and solvable groups by C. Drutu (as  supplemental material)

Feb 10-March 1  Fields  Notes of R. Ash
Assignment 3:   Due March 15 From the notes:  Problems for section 3.2:   2, 5,  6;  Section 3.3 :   5-9;  Section 3.4:   4-8; Section 3.5: 4-7

Solutions to Assignment 3

March 3-24 Galois theory Notes4   
Notes5

Assignment 4: Due March 31 Problems for section 4.2: 1-5; Section 4.4: 3-5;  Section 4.5: 2-5, Section 4.6: 1,2; Section  7.7 :6-10, Find the Galois group of  x^4+4x^2+2. 
Solutions to Assignment 4