On a short exact sequence and extensions of irreducible image-modules

This paper is concerned with the second Loewy layer of the projective cover of an irreducible image-module U, where image is a field of prime characteristic p and G a finite group such that pG. We use elementary cohomological techniques to obtain under certain circumstances a short exact sequence and to relate this second Loewy layer to the set of p-chief factors of the group G. In particular, our results apply if the module U is a projective image-module.