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Maximal subgroups of classical groups in dimensions 16 and 17
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Rogers, Daniel P. (2017) Maximal subgroups of classical groups in dimensions 16 and 17. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3109676~S15
Abstract
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.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Group theory, Maximal subgroups, Finite simple groups, Representations of groups | ||||
Official Date: | February 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Holt, Derek F. | ||||
Sponsors: | Engineering and Physical Sciences Research Council | ||||
Format of File: | |||||
Extent: | ix, 252 leaves : illustrations | ||||
Language: | eng |
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