Citation
Clapham, Paul Charles (1974) Steiner triple systems with blocktransitive automorphism groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10172005105806
Abstract
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If G is an automorphism group of a Steiner triple system which is doubly transitive on the points, then it is transitive on the blocks. It is shown that the converse is false and that all counterexamples have odd order. All Steiner triple systems which have a blocktransitive but not doubly pointtransitive group of automorphisms are described. They include the Euclidean geometries of odd dimension over GF(3), a class of systems first described by Netto in 1893, and another class of systems. A system in this third class has a group of automorphisms acting regularly on the blocks, and the number of points is a prime power congruent to 7 modulo 12. The number of such systems (up to isomorphism) with a prime number of points p, where [...] (mod 12), is shown to be in the interval [...].
The classification of blocktransitive Steiner triple systems is applied to prove the following theorem: if G is a doubly transitive automorphism group of a Steiner triple system and P is a psubgroup of G maximal subject to the condition that it fix more than three points, then the points fixed by P form a subsystem with a doubly transitive automorphism group.
Item Type:  Thesis (Dissertation (Ph.D.)) 

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:  1 May 1974 
Record Number:  CaltechETD:etd10172005105806 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10172005105806 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4125 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  19 Oct 2005 
Last Modified:  26 Dec 2012 03:05 
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