On generalized blocks for alternating groups

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.