Further results on transitive Kirkman triple systems
Let \(X\) be a finite set of cardinality \(v\). A Kirkman triple system \((X, {\mathcal B})\) is called transitive and denoted by \(\text{TKTS}(v)\) if there exists a sharply transitive group \(G\) on \(X\) under which the set of blocks \(\mathcal B\) is invariant, i.e. for any \(\{x, y, z\}\in {\mathcal B}\) and any \(\alpha\in G\), we have \(\alpha(\{x, y, z\})= \{\alpha(x), \alpha(y), \alpha(z)\}\in {\mathcal B}\). This paper contains a new construction for transitive Kirkman triple systems. One of the main results is to show that if there exists a \(\text{TKTS}(3p)\) for any prime \(p\equiv 5\pmod 6\), then for any \(v\equiv 3\pmod 6\) there exists a \(\text{TKTS}(v)\).
scientific article; zbMATH DE number 906657