Citation
Magaard, Kay (1990) The maximal subgroups of the Chevalley groups F4(F) where F is a finite or algebraically closed field of characteristic not equal to 2,3. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd06132007094324
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. We find the conjugacy classes of maximal subgroups of the almost simple groups of type F4(F), where F is a finite or algebraically closed field of characteristic not equal to 2,3. To do this we study F4(F) via its representation as the automorphism group of the 27dimensional exceptional central simple Jordan Algebra J defined over F. A Jordan Algebra over a field of characteristic not equal to 2 is a nonassociative algebra over a field F satisfying xy = yx and [...] = [...] for all its elements x and y. We can represent Aut(F4(F)) on J as the group of semilinear invertible maps preserving the multiplication. Let G = F4(F) and [...]. We have defined a certain subset of proper nontrivial subalgebras as good. The principal results are as follows: SUBALGEBRA THEOREM: Let F be a finite or algebraically closed field of characteristic not equal to 2,3. Let H be a subgroup of [...] and suppose that H stabilizes a subalgebra. Then H stabilizes a good subalgebra. The conjugacy classes and normalizers of good subalgebras are also given. STRUCTURE THEOREM: Let H be a subgroup of [...] such that [...] is closed but not almost simple. Then H stabilizes a proper nontrivial subalgebra or H is contained in a conjugate of [...]. The action of [...] on J is described and it is shown that [...] is unique up to conjugacy in G. THEOREM : If L is a closed simple nonabelian subgroup of G, then [...] is maximal in [...] only if L is one of the following: [...]. For each member [...] we identify those representations [...] which could give rise to a maximal subgroup of G and show the existence of [...] in G. Up to few exceptions we also determine the number of G conjugacy classes for each equivalence class [...].
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  Mathematics 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  16 April 1990 
Record Number:  CaltechETD:etd06132007094324 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd06132007094324 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2575 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  06 Jul 2007 
Last Modified:  26 Dec 2012 02:52 
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