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by [[Richard Brauer]] using modular representation theory played
an important role in early progress towards the
[[classification of finite simple groups]], especially for simple groups whose characterization was not amenable to purely group-theoretic methods because their Sylow 2 subgroups were too small in an appropriate sense. Also, a general result on embedding of elements of 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.
If the characteristic of ''K'' does not divide the order of the group, ''G'', then modular representations are completely reducible, as with ''ordinary''
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