Date: Wednesday, September 12, 2007 Time: 4:00 p.m. Room: FAB 103 Opening Remarks by Robert M. Guralnick University of Southern California Refreshments: 5:00 p.m. in LIT 339

Abstract: In their celebrated theorem, Feit and Thompson (1963) proved that the order of a nonabelian simple finite group is necessarily even: the prime 2 and the 2-subgroups of a simple group play a key role for the structure of the group. More generally, for G a finite group whose order is divisible by a prime number p, how much the collection of p-subgroups of G influences the structure of G has been a key question for group theorists. We shall address some old and recent results along those lines, from Frobenius (1905) to Glauberman (1967), before showing how modern tools of representation theory allow us to understand more about the influence of p-subgroups.

 ^* Professor Broué is an internationally renowned mathematician and one of the leading figures in the field of finite group representations. He has made deep contributions to R. Brauer's theory of p-blocks, including a beautiful conjecture which drives much current research. He studied with Claude Chevalley in Paris. His many honors include the Prix de l'Académie des Sciences and an invited address at the International Congress of Mathematicians (Berkeley, 1986). Professor Broué is Director of L'Institut Henri Poincaré and Editor-in-Chief of the Journal of Algebra.

This History Lecture is one of the featured events of the International Conference on Group Representations and Combinatorics which is taking place during September 10-14, 2007. See the website:
http://qseries.org/~tiep/conf07/.