The Projective Cover of the Trivial Representation for a Finite Group of Lie Type in Defining Characteristic

Abstract

We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.