A Geometric Environment for Building up Loops

Silvia Pianta, Stefano Pasotti, Elena Zizioli

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

1 Citazioni (Scopus)

Abstract

We start from the embedding of the Klein model of a hyperbolic plane H over a Euclidean field K in its direct motion group G=PSL_2(K) and of both in PG(3,K) . We present a geometric procedure to obtain loops which are related to suitable regular subsets of direct motions as transversals of the coset space G/D , where D is the subgroup of hyperbolic rotations fixing a given point o∈H . We investigate some properties of such loops and we determine their automorphism groups.
Lingua originaleEnglish
pagine (da-a)415-426
Numero di pagine12
RivistaResults in Mathematics
DOI
Stato di pubblicazionePubblicato - 2015

Keywords

  • hyperbolic plane
  • loop
  • section
  • transversal

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