History
The earliest work on representation theory over finite fields is by Dickson (1902) who showed that when p does not divide the order of the group then the representation theory is similar to that in characteristic 0. He also investigated modular invariants of some finite groups. The systematic study of modular representations, when the characteristic divides the order of the group, was started by Brauer (1935) and continued by him for the next few decades.
Read more about this topic: Modular Representation Theory
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