Embeddings of resolvable triple systems (Q1971010)

A resolvable triple system of order \(v\) can appear as a subsystem of a resolvable triple system of order \(u\) when \(u=v\) or \(u\geq 3v\), and \(u\) and \(v\) are both multiples of \(3\). When the index is odd, \(u\) and \(v\) must also be odd; and when the index is singly even, \(v\) cannot be \(6\) as no resolvable triple system of order \(6\) exists with singly even index. In this paper it is shown that, with these restrictions, there exists a resolvable triple system of order \(v\) having as a subsystem a resolvable triple system of order \(u\) for each index.