The Projective Cover of the Trivial Module Over a Group Algebra of a Finite Group

• Published in: Communications in algebra Vol. 42; no. 10; pp. 4308 - 4321
• Main Author: Koshitani, Shigeo
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.01.2014
• Subjects: Algebra; Blocking; Byproducts; Classification; Conjugacy class of involutions; Group theory; Loewy length; Mathematical analysis; Modules; Principal block; Projective cover; Socle length

We determine all finite groups G such that the Loewy length (socle length) of the projective cover P(k G ) of the trivial kG-module k G is four, where k is a field of characteristic p > 0 and kG is the group algebra of G over k, by using previous results and also the classification of finite simp...