Geodesic
Nonsplitting F-quasigroups
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 3, pp. 375-381

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

T. Kepka, M.K. Kinyon and J.D. Phillips: The structure of F-quasigroups, J. Algebra 317 (2007), no. 2, 435--461 developed a connection between F-quasigroups and NK-loops. Since NK-loops are contained in the variety generated by groups and commutative Moufang loops, a question that arises is whether or not there exists a nonsplit NK-loop and likewise a nonsplit F-quasigroup. Here we prove that there do indeed exist nonsplit F-quasigroups and show that there are exactly four corresponding nonsplit NK-loops of minimal order $3^6$.
Classification : 20E10, 20N05
Keywords: F-quasigroup; NK-loop; Moufang loop 
@article{CMUC_2012__53_3_a3,
     author = {Gagola III, Stephen},
     title = {Nonsplitting {F-quasigroups}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {375--381},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2012},
     mrnumber = {3017836},
     zbl = {1257.20068},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2012__53_3_a3/}
}
TY  - JOUR
AU  - Gagola III, Stephen
TI  - Nonsplitting F-quasigroups
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2012
SP  - 375
EP  - 381
VL  - 53
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2012__53_3_a3/
LA  - en
ID  - CMUC_2012__53_3_a3
ER  - 
%0 Journal Article
%A Gagola III, Stephen
%T Nonsplitting F-quasigroups
%J Commentationes Mathematicae Universitatis Carolinae
%D 2012
%P 375-381
%V 53
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2012__53_3_a3/
%G en
%F CMUC_2012__53_3_a3
Gagola III, Stephen. Nonsplitting F-quasigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 3, pp. 375-381. http://geodesic.mathdoc.fr/item/CMUC_2012__53_3_a3/