__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)

Jan 27-Feb 8 Nilpotent and Solvable groups, Notes3

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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.

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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