Combinatorial Designs With Prescribed Automorphism Types

Abstract

<p>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?</p> <p>We are able to give a (complete or partial) answer to this question for the following: 1) 3- and 4-rotational Steiner triple systems,</p> <p>2) 3-regular Steiner triple systems,</p> <p>3) Steiner triple systems with an involution fixing precisely three elements,</p> <p>4) 1-rotational triple systems,</p> <p>5) cyclic extended triple systems,</p> <p>6) 1-, 2- and 3-rotational extended triple systems,</p> <p>7) 2-, 3- and 4-regular extended triple systems,</p> <p>8) 1- and 3-rotational directed triple systems,</p> <p>9) 1-rotational Mendelsohn triple systems,</p> <p>10) cyclic extended Mendelsohn triple systems,</p> <p>11) 1-rotational extended Mendelsohn triple systems.</p> <p>We also present a recursive doubling construction for cyclic Steiner quadruple systems, and construct the latter for several orders.</p>