Citation
Berger, Thomas Robert (1967) Class two p groups as fixed point free automorphism groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:11022015081046019
Abstract
Suppose that AG is a solvable group with normal subgroup G where (A, G) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^{c} ≠ r^{d} + 1 for any c = 1, 2 and any prime r where r^{2d+1} divides G and if C_{G}(A) = 1 then the Fitting length of G is bounded by the power of p dividing A.
The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A_{1}, a subgroup of A, where A_{1} centralizes D(R), then all irreducible characters of A_{1}R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.
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:  28 April 1967  
Funders: 
 
Record Number:  CaltechTHESIS:11022015081046019  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:11022015081046019  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9262  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  02 Nov 2015 17:48  
Last Modified:  02 Nov 2015 17:48 
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