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).

Falcone, G., Figula, Á., & Hannusch, C. (2020). Steiner Loops of Affine Type. RESULTS IN MATHEMATICS, 75(4), 1-25 [10.1007/s00025-020-01273-6].

Steiner Loops of Affine Type

Falcone, Giovanni;
2020

Abstract

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).
Settore MAT/03 - Geometria
Falcone, G., Figula, Á., & Hannusch, C. (2020). Steiner Loops of Affine Type. RESULTS IN MATHEMATICS, 75(4), 1-25 [10.1007/s00025-020-01273-6].
File in questo prodotto:
File Dimensione Formato  
Falcone2020_Article_SteinerLoopsOfAffineType (2).pdf

accesso aperto

Descrizione: Articolo
Dimensione 567.22 kB
Formato Adobe PDF
567.22 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/438455
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact