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The Maximal Subgroups of the Low-Dimensional Finite Classical Groups by Colva M. Roney-Dougal, Derek F. Holt, John N. Bray

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5Groups in Class image: defining characteristic

The theory of representations of finite simple groups of Lie type in defining characteristic is somewhat advanced. The representations arise from those of the associated algebraic groups, and so some familiarity with the theory of algebraic groups is necessary in order to understand it. For an introduction to this theory see, for example, the survey article by Humphreys [51]. The enthusiastic reader may wish to consult Jantzen [58] for a more detailed exposition. Humphrey’s classic book [50] provide a general exposition of the theory of algebraic groups and their representations, whilst Malle and Testerman’s ...

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