What is defect group?

Some articles on group, groups, defect group:

Richard Brauer - Mathematical Work
... induction theorem, which has applications in number theory as well as finite group theory, and its corollary Brauer's characterization of characters, which is central to ... in 1956, later provided significant impetus towards the classification of finite simple groups, for it implied that there could only be finitely many finite simple ... theory to obtain subtle information about group characters, particularly via his three main theorems ...
Brauer's Three Main Theorems - 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 ... 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 ...

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