## Representation of quasiregular configurations.(Russian. English summary)Zbl 0731.51003

This paper continues the work by the first of the authors [Rend. Ist. Mat. Univ. Trieste 2, 139-145 (1970; Zbl 0213.220)] concerning the representations of free projective planes in the three-dimensional projective space. Here the focus is on finite quasiregular configurations and the following two main results are proved: (1) Any quasi-regular configuration $${\mathcal K}$$ is representable in the three-dimensional projective space $$\pi_ 3(F)$$ over a field F of characteristic 0, and (2) any quasiregular configuration $${\mathcal K}$$ that is locally representable in a Desarguesian plane is representable in the projective plane $$\pi_ 2(F)$$ over an algebraically closed field F of characteristic 0, as well.
Reviewer: J.Libicher (Brno)

### MSC:

 51A30 Desarguesian and Pappian geometries 51A45 Incidence structures embeddable into projective geometries 05B30 Other designs, configurations 51E14 Finite partial geometries (general), nets, partial spreads

Zbl 0213.220
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