sentences:  Brauer's three main theorems
  
  Brauer's main theorems are three theorems in representation theory of finite groups linking the blocks of a finite group (in characteristic "p") with those of its "p"-local subgroups, that is to say, the normalizers of its non-trivial "p"-subgroups.The second and third main theorems allow refinements of orthogonality relations for ordinary characters which may be applied in finite group theory.