Professor: George
Seelinger

Office: Stevenson 313C (Enter through STV 313)

Phone: 438-8781

email: gfseeli@ilstu.edu

Office Hours: TBA

**CATALOG DESCRIPTION:** Group theory including the Sylow theorems and
other advanced topics; ring theory.

Prerequisites: MAT 336 or consent of
instructor.

**TEXT:** *Abstract
Algebra*, by D. Dummit and R. Foote, 3rd Edition,
Wiley, 2004.
(Errata Page in PDF format)

**COURSE WEB PAGE:** http://www.math.ilstu.edu/gfseeli/mat407/

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CLASS NOTES (These class notes will be updated throughout the semester.)

**ABOUT THE COURSE:** This course is intended as a follow up to an
introductory course in group theory. We will review some of the introductory material about groups in Chapters 0 through 2, then go on to study more about the structure of groups with an emphasis on finite groups, including studying group actions and the Sylow Theorems. Further topics in group theory will be
covered as well as an introduction to ring theory as time permits.

As a class, we will meet at the scheduled 2:00-3:50 time on Mondays, but this will be supplemented by informal meeting times that will be arranged based on the schedules of the class members and will be set up the first week of class.

**GRADING:** In this course, you will be graded on weekly homework assignments (50%), a mid-term exam (20%), and a final exam (30%).

**EXAMS:** The mid-term exam will be a take-home exam that will be
distributed on Monday, March 15th and be due the following Monday, March 22nd. The in-class portion of the final exam is scheduled for Wednesday,
May 5, from 3:10 to 5:10.

**HOMEWORK:** Homework will be assigned weekly and collected the following week. Homework problems will be chosed to allow students to probe
further into the algebraic concepts we will be covering and allow for further
discussion of these topics. Proofs on these homeworks should be written in a
clear style and will be graded for both correctness and clarity.

**Homework Assignments:**

__Due Jan 25__: Exercises 1 - 9 of notes

__Due Feb 1__: Exercises 10 - 16 of notes

__Due Feb 11__: Exercises 17 - 23 of notes

__Due Feb 15__: Exercises 24, 25 of notes, Dummit and Foote p. 85 #7, p. 95 # 8, p. 96 # 11. Also, find all subgroups (with lattice diagrams) for
**Z**_{2} x **Z**_{5},
**Z**_{2} x **Z**_{6}, and *D*_{12}.

__Due Feb 22__: pp. 86-88 #4,17,29, p. 96 #12, 18, 19, p. 101 # 3, 4

__Due March 4__: p. 89 # 36, 38; p. 96 # 16; p.101 # 7

__Due March 29__: pp. 146-148 # 7, 9
(Assume **F**_{3} is **Z**_{3}), 16, 21, 27, 33

(Hint for #27: Let N, P, and Q be Sylow 3, 5, and 7 subgroups of G. First
show NP and NQ are abelian subgroups. Once this is done, you can show N is in the center of G.)

__Due April 5__: Homework 8.

__Due April 15__: Homework 9

__Due April 22__: Homework 10

**Algebra on the WEB:**

The Development of Group
Theory (Article by: J J O'Connor and E F Robertson)

Groups 15 by John Wavrick of UC San Diego. This program allows
you to make computations for groups with at most 15 elements.

A discussion of Rubik's Cube Groups can be found at
the Dog School of Mathematics.

The Development of Ring Theory
(Article by: J J O'Connor and E F Robertson)

First 1000 Primes

The Great Internet Mersenne Prime Search Project (GIMPS)

The Millennium Problems posed by the
Clay Mathematics Institute.