Math 732 — Spring 2001 Topics in Group Theory

Prerequisite: A previous course in group theory (e.g., Math 434 or Math 631).

This course should be accessible to beginning graduate students and will be of interest to students of algebra, representation theory, algebraic topology, among others.

The course might well be titled "a second course in group theory'' as basic results about groups (groups acting on sets, Sylow theorems, etc.) will be assumed. Any other necessary background from elementary group theory (wreath products, ...) will be summarized or developed in class as needed.

Probable topics include the following:

• Schur-Zassenhaus theorem
• Solvable groups - the theory of P. Hall
• Permutation groups
• Mathieu groups
• Transfer and fusion, Alperin's theorem
• Thompson subgroup, Thompson complement theorem
• Group characters
• Frobenius groups

There will be no text for the course.

Some suggested references:

M. Aschbacher, Finite group theory, Cambridge studies in advanced mathemtatics, 10, CUP, 1986.

J. D. Dixon & B. Mortimer, Permutation groups, GTM 163, Springer-Verlag, 1996.

L. C. Grove, Groups and characters, Wiley, 1997.

H. Kurzweil, Bernd Stellmacher, Theorie der endlichen Gruppen, Springer-Verlag, 1998.

B. A. F. Wehrfritz, Finite groups: A second course on group theory, World Scientific, 1999.