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Title: Maximal subgroups of classical groups in dimensions 16 and 17
Author: Rogers, Daniel P.
ISNI:       0000 0004 6496 0238
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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Aschbacher's Theorem [1] subdivides maximal subgroups of the classical groups and their almost simple extensions into nine classes, denoted C1,…,C9. The first eight of these classes contain the so-called `geometric-type' subgroups. Members of these classes have been classified fully for classical groups in dimensions 13 and higher in [33], and in the low-dimensional case in [8]. Class C9, or S, consists of groups which are almost simple modulo their centre. There is currently no description of all members of this class in all dimensions. In [8], the authors describe all members of class S in dimensions up to 12, and in [48] the author describes these in dimensions 13 - 15. In this thesis, we will extend these results to determine the members of class S in dimensions 16 and 17 (and thus all maximal subgroups of classical groups in these dimensions) except in the case of the orthogonal groups where some results are conjectured. Chapter 1 provides background information, including the subdivision of class S into subclasses S1 and S2. Chapters 3 and 4 describe the members of S1 and S2 respectively for 16- and 17-dimensional classical groups, and Chapter 6 describes containments between these classes. The list of maximal subgroups is summarised in Chapter 7. We also provide some general results which can be applied to members of class S in classical groups of other dimensions. Chapter 2 discusses results which can be applied to a class of S2-candidate subgroups whose field automorphism is induced by a permutation matrix. In Chapter 5 we provide a construction of the natural representation of the spin and half-spin groups and their normalisers.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics