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
Famous quotes containing the words theorem and/or main:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)
“The chief misery of the decline of the faculties, and a main cause of the irritability that often goes with it, is evidently the isolation, the lack of customary appreciation and influence, which only the rarest tact and thoughtfulness on the part of others can alleviate.”
—Charles Horton Cooley (1864–1929)