MATH 463 Group Theory (Fall 2008)

2008 - 09 Fall

MATH 463: Introduction to Group Theory

(Not finalized yet; there will be changes and additions!)

Many who have had an opportunity of knowing any more about mathematics confuse it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination. --- Sofia Kovalevskaya
(taken from http://www-history.mcs.st-andrews.ac.uk/Quotations/Kovalevskaya.html)

Announcements:

The exams are on 19 November and 23 December at 17.40.
Subscribe to the discussion list of the course.
The first lecture will be on 18 September 2008, Thursday.
Students of MATH 463, please check this page regularly.

Lectures:
Monday 10:40-12:30 (M-103) Thursday 10:40-11:30 (M-103)

Books:

Main Text: "Topics in group theory" by Geoff Smith and Olga Tabachnikova, Springer, 2000.
Undergraduate Oriented Books:
- "A course in group theory" by John F. Humphreys, Oxford University Press, 1996.
- "Adventures in group theory" by David Joyner, Johns Hopkins University Press, 2002.
Graduate Oriented Books:
- "The Theory of Finite Groups" by Hans Kurzweil and Bernd Stellmacher, Springer-Verlag, 2004.
- "Fundamentals of the Theory of Groups" by M. I. Kargapolov and J. I. Merzljakov, Springer Verlag, 1979
- "A Course in the Theory of Groups" by D. Robinson, Springer Verlag, 1996.
- "The Theory of Groups" by J. J. Rotman, Allyn and Bacon, 1973.
To review the group theory part of MATH 367:
- "Groups and Symmetry" by M. A. Armstrong, Springer Verlag, 1988. (I recommend this book very strongly.)
- "Groups for Undergraduates" by J. A. Moody, World Scientific, 1994.

Topics

A quick review of MATH 367 (Subgroups, cyclic groups, cosets, quotient groups, homomorphisms etc.)

Abelian groups (Finite abelian groups, finitely generated abelian groups, divisible abelian groups etc.)

Actions

Sylow Theorems (with proofs) and some applications

Some classifications (groups of order less than 30, simple groups of order 168 etc.)

Solvable and nilpotent groups