Kirkman triple systems of order 21 with nontrivial automorphism group

Kirkman Triple Systems of Orders 27 , 33 , and 39

In the search for doubly resolvable Kirkman triple systems of order v, systems admitting an automorphism of order (v 3)=3 fixing three elements, and acting on the remaining elements in three orbits of length (v 3)=3, have been of particular interest. We have established by computer that 100 such Kirkman triple systems exist for v = 21, 81,558 for v = 27, at least 4,494,390 for v = 33, and at le...

Steiner Triple Systems of Order 19 with Nontrivial Automorphism Group

There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in pract...

Automorphisms of Steiner triple systems

Abstract: Steiner triple systems are among the simplest and most intensively studied combinatorial designs. Their origins go back to the 1840s, and there exists by now a sizeable literature on the topic. In 1980, Babai proved that almost all Steiner triple systems have no nontrivial automorphism. On the other hand, there exist Steiner triple systems with large automorphism groups. We will discu...

Kirkman Triple Systems of Orders 21 and 27

The Automorphism Groups of Steiner Triple Systems Obtained by the Bose Construction

The automorphism group of the Steiner triple system of order v ≡ 3 (mod 6), obtained from the Bose construction using any Abelian Group G of order 2s + 1, is determined. The main result is that if G is not isomorphic to Zn 3 × Zm 9 , n ≥ 0, m ≥ 0, the full automorphism group is isomorphic to Hol(G)× Z3, where Hol(G) is the Holomorph of G. If G is isomorphic to Zn 3 × Zm 9 , further automorphism...