Controlled blocks of the finite quasisimple groups for odd primes

Abstract

We classify controlled blocks, introduced by Alperin and Broué in 1979 for all quasi-simple groups G for odd primes. The results imply that every nilpotent block of G has abelian defect groups, which in turn is one of the main results proved by An and Eaton in a paper of 2011. We also give an explicit characterization of non-controlled blocks of all quasi-simple groups G for odd primes. This implies the block theoretic analogue of Glauberman’s ZJ -theorem for G proved by Kessar, Linckelmann and Robinson in 2002. Hence we reduced the problem of the study of controlled blocks of G to that of Broué's abelian conjecture. The journal is a leading scholarly journal in mathematics.