Quasigroups arisen by right nuclear extension

Nagy, Péter T., and Stuhl, Izabella. "Quasigroups arisen by right nuclear extension." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 391-395. <http://eudml.org/doc/246115>.

@article{Nagy2012,
abstract = {The aim of this paper is to prove that a quasigroup $Q$ with right unit is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by the factor quasigroup $Q/G$ if and only if there exists a normalized left transversal $\Sigma \subset Q$ to $G$ in $Q$ such that the right translations by elements of $\Sigma $ commute with all right translations by elements of the subgroup $G$. Moreover, a loop $Q$ is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by a loop if and only if $G$ is middle-nuclear, and there exists a normalized left transversal to $G$ in $Q$ contained in the commutant of $G$.},
author = {Nagy, Péter T., Stuhl, Izabella},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {extension of quasigroups; right nucleus; quasigroup with right unit; transversal; extensions of quasigroups; nuclei; quasigroups with right unit; transversals; cosets},
language = {eng},
number = {3},
pages = {391-395},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasigroups arisen by right nuclear extension},
url = {http://eudml.org/doc/246115},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Nagy, Péter T.
AU - Stuhl, Izabella
TI - Quasigroups arisen by right nuclear extension
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 3
SP - 391
EP - 395
AB - The aim of this paper is to prove that a quasigroup $Q$ with right unit is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by the factor quasigroup $Q/G$ if and only if there exists a normalized left transversal $\Sigma \subset Q$ to $G$ in $Q$ such that the right translations by elements of $\Sigma $ commute with all right translations by elements of the subgroup $G$. Moreover, a loop $Q$ is isomorphic to an $f$-extension of a right nuclear normal subgroup $G$ by a loop if and only if $G$ is middle-nuclear, and there exists a normalized left transversal to $G$ in $Q$ contained in the commutant of $G$.
LA - eng
KW - extension of quasigroups; right nucleus; quasigroup with right unit; transversal; extensions of quasigroups; nuclei; quasigroups with right unit; transversals; cosets
UR - http://eudml.org/doc/246115
ER -