Geodesic
Direct Product of Derived Steiner Systems Using Inversive Planes
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1365-1369

Voir la notice de l'article provenant de la source Cambridge University Press

A Steiner system S(t, k, v) is a pair (P, B) where P is a v-set and B is a collection of k-subsets of P (usually called blocks) such that every t-subset of P is contained in exactly one block of B. As is well known, associated with each point x ∈ P is a S(t � 1, k � 1, v � 1) defined on the set Px = P\{x} with blocks B(x) = {b\{x}|x ∈ b and b ∈ B}.The Steiner system (Px , B(x)) is said to be derived from (P, B) and is called (obviously) a derived Steiner (t – 1, k – 1)-system. Very little is known about derived Steiner systems despite much effort (cf. [11]). It is not even known whether every Steiner triple system is derived.Steiner systems are closely connected to equational classes of algebras (see [7]) for certain values of k. 
Phelps, K. T. Direct Product of Derived Steiner Systems Using Inversive Planes. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1365-1369. doi: 10.4153/CJM-1981-105-7
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