In this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a powerful method for constructing Steiner triple systems containing Veblen points.
Giovanni Falcone, Agota Figula, Mario Galici (2025). Extensions of Steiner Triple Systems. JOURNAL OF COMBINATORIAL DESIGNS [10.1002/jcd.21964].
Extensions of Steiner Triple Systems
Giovanni Falcone;Mario Galici
2025-01-01
Abstract
In this article, we study extensions of Steiner triple systems by means of the associated Steiner loops. We recognize that the set of Veblen points of a Steiner triple system corresponds to the center of the Steiner loop. We investigate extensions of Steiner loops, focusing in particular on the case of Schreier extensions, which provide a powerful method for constructing Steiner triple systems containing Veblen points.
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