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 originale | English |
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pagine (da-a) | 415-426 |
Numero di pagine | 12 |
Rivista | Results in Mathematics |
DOI | |
Stato di pubblicazione | Pubblicato - 2015 |
Keywords
- hyperbolic plane
- loop
- section
- transversal