2017/02/21 by Shigeo Koshitani, Caroline Lassueur
Mathematics · #Abelian group #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Block (permutation group theory) #Classification of finite simple groups #Combinatorics #Computer science #Finite Group Theory Research #Finite group #Group (periodic table) #Group of Lie type #Group theory #Mathematics #Principal (computer security) #Pure mathematics #Quiver #Simple (philosophy) #Simple group #Simple module #Sylow theorems #math.RT #msc:16G70 #msc:20C20
paper · pdf · doi:10.1017/nmj.2017.45
19pages
arxiv created 2017/02/21 · openalex publication_date 2018/02/05 · arxiv updated 2020/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Given an odd prime p , we investigate the position of simple modules in the stable Auslander–Reiten quiver of the principal block of a finite group with noncyclic abelian Sylow p -subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is 3 , we prove that simple modules in the principal block all lie at the end of their components.