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Title: Maximal tori in finite groups of Lie type
Author: Gager, Philip Charles
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1973
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It is believed that a unified approach to a study of the representation theory of the finite groups of Lie type should begin with a study of the regular characters of the maximal tori of these groups. This thesis is directed towards determining the structure of the maximal tori in the finite groups of Lie type. Chapter 1 is a general introduction to the properties of Chevalley groups, together with the consequences of a result of Springer and Steinberg. This result establishes a correspondence between the conjugacy classes of maximal tori and certain equivalence classes of the associated Weyl group. In certain cases, these classes are the conjugacy classes, and Chapter 2 begins with a review of Carter's unified approach to the conjugacy classes of Weyl groups. Chapter 2 also includes some results on automorphisms of Weyl groups in relation to Carter's approach. The finite Chevalley groups are the first to be considered. Chapter 3 studies those of type Al, and Chapter 4 simultaneously considers the Chevalley groups of types Bl, Cl and Dl. Finally, Chapter 5 presents the results for the Chevalley groups of exceptional type. The finite groups of twisted type are the last to be discussed. Chapter 6 begins with a general description of the classes of the Weyl group in these types and concludes with the results for-the Steinberg groups of types 2Al, 2Dl and 2E6. The Steinberg groups of type 3D4 are left until the end of Chapter 7, after a discussion of the Ree and Suzuki groups. The thesis concludes with a note on the representation theory and a description of the regular characters of the maximal tori.
Supervisor: Not available Sponsor: Science Research Council ; University of Warwick
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics