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His most famous result is his joint, with John G. Thompson, proof of the Feit–Thompson theorem that all finite groups of odd order are solvable. At the time it was written, it was probably the most complicated and difficult mathematical proof ever completed. He wrote almost a hundred other papers, mostly on finite group theory, character theory (in particular introducing the concept of a coherent set of characters), and modular representation theory. Another regular theme in his research was the study of linear groups of small degree, that is, finite groups of matrices in low dimensions. It was often the case that, while the conclusions concerned groups of complex matrices, the techniques employed were from modular representation theory.
He also wrote the books: The representation theory of finite groupsISBN 0-444-86155-6 and Characters of finite groups, which are now standard references on character theory, including treatments of modular representations and modular characters.