Search results for "Triple system"

showing 2 items of 12 documents

An algebraic representation of Steiner triple systems of order 13

2021

Abstract In this paper we construct an incidence structure isomorphic to a Steiner triple system of order 13 by defining a set B of twentysix vectors in the 13-dimensional vector space V = GF ( 5 ) 13 , with the property that there exist precisely thirteen 6-subsets of B whose elements sum up to zero in V , which can also be characterized as the intersections of B with thirteen linear hyperplanes of V .

Steiner triple systemZero (complex analysis)Steiner triple system STS Additive block designSTSCombinatoricsSet (abstract data type)Steiner systemIncidence structureHyperplaneSettore MAT/05 - Analisi MatematicaAlgebra representationQA1-939Order (group theory)Settore MAT/03 - GeometriaMathematicsVector spaceMathematicsAdditive block designExamples and Counterexamples
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Steiner Loops of Affine Type

2020

Steiner loops of affine type are associated to arbitrary Steiner triple systems. They behave to elementary abelian 3-groups as arbitrary Steiner Triple Systems behave to affine geometries over GF(3). We investigate algebraic and geometric properties of these loops often in connection to configurations. Steiner loops of affine type, as extensions of normal subloops by factor loops, are studied. We prove that the multiplication group of every Steiner loop of affine type with n elements is contained in the alternating group An and we give conditions for those loops having An as their multiplication groups (and hence for the loops being simple).

Steiner triple systems steiner loops of affine type multiplication groups of loops finite geometries commutative Moufang loop.Settore MAT/03 - Geometria
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