Simple modules in the Auslander-Reiten quiver of principal blocks with abelian defect groups

Shigeo Koshitani, Caroline Lassueur

Published 2017-02-17Version 1

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 non-cyclic 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