COLLOQUIUM

DEPARTMENT OF MATHEMATICS AND STATISTICS

OAKLAND UNIVERSITY

ROCHESTER, MICHIGAN  48309

Hung Ngoc Nguyen

Michigan State University

E. Lansing, MI

Permutation Modules of the Finite Classical Groups

Abstract

Given a Group G acting on a set and a field F, the problem of determining the structure of the permutation FG-module has been studied extensively for many years.  In particular, permutation modules as well as permutation representations for finite classical groups have obtained significant attention.

Suppose that G is a finite classical group.  The permutation module for the natural action of G on singular points of its standard module has been studied in great depth in the work of Higman, Liebeck, Lataille, Sin, and Tiep.  However, not much has been known about the action of G on nonsingular points.  In this talk, we first survey some known results about rank 3 permutation modules in general and then describe some recent results about rank 3 permutation modules for finite classical groups acting on nonsingular points.  The talk is intended for a general audience.

Tuesday, April 6, 2010

3:00 – 4:00 P.M.

372 Science and Engineering Building

(Refreshments at 2:30-3:00 PM in the kitchen area adjacent to 368 SEB)