Controlled 2-blocks of quasisimple groups

Abstract

Controlled p-blocks, introduced by Alperin and Broué in 1979, were classified for quasisimple groups G for odd primes in [10]. We classify the controlled 2-blocks of quasisimple groups G. The results imply that every nilpotent 2-block of G has abelian defect groups. This agrees with one of the main results proved in [15]. We also give an explicit characterization of non-controlled 2-blocks of all quasisimple groups. This implies that the p=2 version of the block theoretic analogue of Glauberman's ZJ-theorem, proved by Kessar, Linckelmann and Robinson in [27], holds for quasisimple groups G.