We investigate the nilpotent blocks of positive defect, introduced by Broué and Puig in 1980 for the quasisimple groups for odd primes. In particular, it is shown that every nilpotent block of a quasisimple group has abelian defect groups. A conjecture of Puig concerning the recognition of nilpotent blocks is also shown for these groups. The is one of the top journals in mathematics.
