Abstract
This chapter presents Brauer's first, second, and third main theorems on blocks, Fong's theory of block covering, and related results. For every principal indecomposable RH (respectively, FH)-module W belonging to b, there exist a principal indecomposable RG (respectively, FG)-module V such that W/VH. Principal indecomposable RH-modules are in one-to-one correspondence to principal indecomposable FH-modules via the reduction mod π. Thus, it suffices to prove the assertion in the case where W is a principal indecomposable FH-module.
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