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. These do not presently admit a proof purely in terms of ordinary characters. All three main theorems are stated in terms of the Brauer correspondence.
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