We study oriented Steiner loops L which are strictly related to oriented Steiner triple systems and discuss thoroughly the interplay between the structure of these Steiner triple systems and the properties of L. We describe the groups generated by the left, right and all translations of L and show how the group of automorphisms of L is related to the automorphism group and to the blocking subsystems of the corresponding Steiner triple system. In the final section we classify the non-rigid oriented Steiner loops of order 16 and 20.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology