Abstract:
The classification of blocks with special defect groups is one of the main problems in the modular representations theory. In work on nilpotent and controlled blocks of finite quasi-simple groups, we notice that blocks with extra-special defect groups play a special role. In particular it turns out that almost all controlled blocks with nonabelian defect groups of a quasi-simple group have extraspecial or trivial intersection defect groups. So we classify all blocks of finite quasi-simple groups with extra-special defect groups. Top journal in the field.