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

✍ Scribed by Conchita Martı́nez-Pérez

• Book ID: 104152331
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 118 KB
• Volume: 161
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00092-x

✦ Synopsis

This paper is concerned with the second Loewy layer of the projective cover of an irreducible KG-module U , where K is a ÿeld of prime characteristic p and G a ÿnite group such that p||G|. 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 KG=CG(U )-module.