Brauer's First Main Theorem
Brauer's first main theorem (Brauer 1944, 1956, 1970) states that if is a finite group a is a -subgroup of, then there is a bijection between the set of (characteristic p) blocks of with defect group and blocks of the normalizer with defect group D. This bijection arises because when, each block of G with defect group D has a unique Brauer correspondent block of H, which also has defect group D.
Read more about this topic: Brauer's Three Main Theorems
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