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{{Short description| Studies linear representations of finite groups over a field K of positive characteristic p}}
'''Modular representation theory''' is a branch of [[mathematics]], and
Within finite group theory, [[character theory|character-theoretic]] results proved by [[Richard Brauer]] using modular representation theory played an important role in early progress towards the [[classification of finite simple groups]], especially for [[simple group]]s whose characterization was not amenable to purely group-theoretic methods because their [[Sylow's theorems|Sylow 2-subgroup]]s were too small in an appropriate sense. Also, a general result on embedding of elements of [[order (group theory)|order]] 2 in finite groups called the [[Z* theorem]], proved by [[George Glauberman]] using the theory developed by Brauer, was particularly useful in the classification program.
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