Additive Steiner triple systems

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Abstract

A Steiner triple system is additive if it can be embedded in a commutative group in such a way that the sum of the three points in any given block is zero.In this paper we show that a Steiner triple system is additive if and only if it is the point-line design of either a projective space PG(d,2) over GF(2) or an affine space AG(d,3) over GF(3), for d ≥ 1. Our proof is based on algebraic arguments and on the combinatorial characterization of finite projective geometries in terms of Veblen points.
Lingua originaleEnglish
Titolo della pubblicazione ospiteBollettino di matematica pura e applicata, Vol. VII
Pagine9-15
Numero di pagine7
Stato di pubblicazionePublished - 2014

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Pavone, M. (2014). Additive Steiner triple systems. In Bollettino di matematica pura e applicata, Vol. VII (pagg. 9-15)