Date of Award
Doctor of Philosophy (PhD)
Dr. Alexander Rosa
In this thesis we deal with the following question: given a permutation α on a set V, does there exist a certain block design on V admitting α as an automorphism?
We are able to give a (complete or partial) answer to this question for the following: 1) 3- and 4-rotational Steiner triple systems,
2) 3-regular Steiner triple systems,
3) Steiner triple systems with an involution fixing precisely three elements,
4) 1-rotational triple systems,
5) cyclic extended triple systems,
6) 1-, 2- and 3-rotational extended triple systems,
7) 2-, 3- and 4-regular extended triple systems,
8) 1- and 3-rotational directed triple systems,
9) 1-rotational Mendelsohn triple systems,
10) cyclic extended Mendelsohn triple systems,
11) 1-rotational extended Mendelsohn triple systems.
We also present a recursive doubling construction for cyclic Steiner quadruple systems, and construct the latter for several orders.
Cho, Chung Je, "Combinatorial Designs With Prescribed Automorphism Types" (1983). Open Access Dissertations and Theses. Paper 1414.