Steiner Loops of Affine Type

Giovanni Falcone, Carolin Hannusch, Ágota Figula

Research output: Contribution to journalArticlepeer-review


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).
Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalResults in Mathematics
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Applied Mathematics


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