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