Geodesic
Ternary quasigroups and the modular group
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 309-317

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

For a positive integer $n$, the usual definitions of $n$-quasigroups are rather complicated: either by combinatorial conditions that effectively amount to Latin $n$-cubes, or by $2n$ identities on $n+1$ different $n$-ary operations. In this paper, a more symmetrical approach to the specification of $n$-quasigroups is considered. In particular, ternary quasigroups arise from actions of the modular group.
Classification : 08A68, 20N05, 20N15, 20N20
Keywords: quasigroup; ternary quasigroup; $n$-quasigroup; heterogeneous algebra; hyperidentity; modular group; conjugate; parastrophe; time reversal 
@article{CMUC_2008__49_2_a12,
     author = {Smith, Jonathan D. H.},
     title = {Ternary quasigroups and the modular group},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {309--317},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2008},
     mrnumber = {2426895},
     zbl = {1192.20064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a12/}
}
TY  - JOUR
AU  - Smith, Jonathan D. H.
TI  - Ternary quasigroups and the modular group
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2008
SP  - 309
EP  - 317
VL  - 49
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a12/
LA  - en
ID  - CMUC_2008__49_2_a12
ER  - 
%0 Journal Article
%A Smith, Jonathan D. H.
%T Ternary quasigroups and the modular group
%J Commentationes Mathematicae Universitatis Carolinae
%D 2008
%P 309-317
%V 49
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a12/
%G en
%F CMUC_2008__49_2_a12
Smith, Jonathan D. H. Ternary quasigroups and the modular group. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 2, pp. 309-317. http://geodesic.mathdoc.fr/item/CMUC_2008__49_2_a12/