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Let G=GL(n,q), SL(n,q) or PGL(n,q) where q is a power of some prime number p,let U denote a Sylow p-subgroup of G and let R be a commutative ring in which pis invertible. Let D(U) denote the derived subgroup of U and let e be thecentral primitive idempotent of the group algebra RD(U) corresponding to theprojection on the invariant RD(U)-submodule. The aim of this note is to provethat the R-algebras RG and eRGe are Morita equivalent (through the naturalfunctor sending an RG-module M to the eRGe-module eM).

A progenerator for representations of SL(n,q) in transverse characteristic