When is it hard to show that a quasigroup is a loop?

Keedwell, Anthony Donald. "When is it hard to show that a quasigroup is a loop?." Commentationes Mathematicae Universitatis Carolinae 49.2 (2008): 241-247. <http://eudml.org/doc/250476>.

@article{Keedwell2008,
abstract = {We contrast the simple proof that a quasigroup which satisfies the Moufang identity $(x\cdot yz)x = xy\cdot zx$ is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity $(xy\cdot z)y=x(y\cdot zy)$ is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.},
author = {Keedwell, Anthony Donald},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Moufang quasigroups; Moufang loops; identities of Bol-Moufang type; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties},
language = {eng},
number = {2},
pages = {241-247},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {When is it hard to show that a quasigroup is a loop?},
url = {http://eudml.org/doc/250476},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Keedwell, Anthony Donald
TI - When is it hard to show that a quasigroup is a loop?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 2
SP - 241
EP - 247
AB - We contrast the simple proof that a quasigroup which satisfies the Moufang identity $(x\cdot yz)x = xy\cdot zx$ is necessarily a loop (Moufang loop) with the remarkably involved prof that a quasigroup which satisfies the Moufang identity $(xy\cdot z)y=x(y\cdot zy)$ is likewise necessarily a Moufang loop and attempt to explain why the proofs are so different in complexity.
LA - eng
KW - Moufang quasigroups; Moufang loops; identities of Bol-Moufang type; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties
UR - http://eudml.org/doc/250476
ER -