On generalized blocks for alternating groups

Abstract

In a recent paper Külshammer, Olsson, Robinson gave a d-analogue for the Nakayama conjecture for symmetric groups where d 2 is an arbitrary integer. We prove that there is a natural d-analogue of the Nakayama conjecture for alternating groups whenever d is 2 or an arbitrary odd integer greater than 1. This generalizes an old result of Kerber.

On defect groups for generalized blocks of the symmetric group

“…Following this work, A. Maróti studied generalized blocks in the alternating groups, and proved that, if ℓ is 2 or any odd integer greater than 1, then the ℓ-blocks of the alternating groups also satisfy an analogue of the Nakayama Conjecture (cf [8]).…”

Generalized Blocks of Unipotent Characters in the Finite General Linear Group

“…Following this work, A. Maróti studied generalized blocks in the alternating groups, and proved that, if ℓ is 2 or any odd integer greater than 1, then the ℓ-blocks of the alternating groups also satisfy an analogue of the Nakayama Conjecture (cf [9]). …”