On a conjecture of G. Malle and G. Navarro on nilpotent blocks. (Q648411)

Summary: In a recent article [Trans. Am. Math. Soc. 363, No. 12, 6647-6669 (2011; Zbl 1277.20013)], \textit{G. Malle} and \textit{G. Navarro} conjectured that the \(p\)-blocks of a finite group all of whose height 0 characters have the same degree are exactly the nilpotent blocks defined by M. Broué and L. Puig. In this paper, we check that this conjecture holds for spin-blocks of the covering group \(2.\mathfrak A_n\) of the alternating group \(\mathfrak A_n\), thereby solving a case excluded from the study of quasi-simple groups by Malle and Navarro.