Abstract:
A transformation of Steiner quadruple systems $S(v,4,3)$ is introduced. For a given system, it allows to construct new systems of the same order, which can be nonisomorphic to the given one. The structure of Steiner systems $S(v,4,3)$ is considered. There are two different types of such systems, namely, induced and singular systems. Induced systems of 2-rank $r$ can be constructed by the introduced transformation of Steiner systems of 2-rank $r-1$ or less. A sufficient condition for a Steiner system $S(v,4,3)$ to be induced is obtained.