Use this URL to cite or link to this record in EThOS:
Title: Combinatorial designs and their automorphism groups
Author: Lovegrove, Graham John
ISNI:       0000 0004 2673 4539
Awarding Body: Open University
Current Institution: Open University
Date of Award: 2009
Availability of Full Text:
Access from EThOS:
Access from Institution:
This thesis concerns the automorphism groups of Steiner triple systems and of cycle systems. Although most Steiner triple systems have trivial automorphism groups [2], it is widely known that for every abstract group, there exists a Steiner triple system whose automorphism is isomorphic to that group [16]. The well-known Bose construction [4] for Steiner triple systems, which has a number of variants, has a particularly nice structure, which makes it possible to say much about the automorphism group, and in the case of the construction based on an Abelian group, to derive the full automorphism group. The thesis contains a full analysis of these matters. Some of these results have been published by the author in [14]. The thesis also proves new results concerning the automorphism group for Steiner triple systems constructed using the tripling construction. An m-cycle system is a decomposition of a complete graph into cycles of length m. A Steiner triple system is thus a 3-cycle system. The thesis proves the result that for all m > 3, and for each abstract finite group, there exists an m-cycle system whose automorphism group is isomorphic to that group. In addition, the thesis contains a collection of new results concerning the conjecture by Furedi that every Steiner triple system is decomposable into triangles. Although this conjecture is expected to remain open for some time, it is possible to prove it for a number of standard constructions. It is further shown that for sufficiently large v, the number of Steiner triple systems of order v that are decomposable into triangles is at least vv2(1/54-0(1)).
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral