@article{728ca4af915d416eb2776f769e3168bb,
title = "The Geometry of Point Reflections and Quasigroups",
abstract = "This is a survey of results from the rich theory of medial and more general quasigroups and its close connection with the geometry of point-reflections. The emphasis is on questions regarding the simplest axiomatization, in the sense of the minimal number of variables appearing in the identtties, on dependence or independence of axioms, and on representation theorems in the style of Toyoda.",
keywords = "Point-reflections, left Bruck loop, medial property, moufang loop, quasigroup, simple axiomatization",
author = "Yuri Movsisyan and Victor Pambuccian",
note = "Funding Information: This paper was written while the second author was a Fulbright Scholar at Yerevan State University. The first author{\textquoteright}s research was partially supported by the State Committee of Science of the Republic of Armenia, Grants 10-3/1-41, 18T-1A306. Thanks are due to Stephan Schulz for assistance with the automatic theorem prover E, to Tom{\'a}{\v s} Kepka for pointing out the existence of nonassociative commutative Moufang loops of order 81, to Michael Kinyon for having provided the model of independence of S mentioned in Sect. and for having answered several questions, and to the anonymous referee for many improvements and for having provided greatly simplified proofs carried out by the automatic theorem prover PROVER9. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",
year = "2020",
month = dec,
day = "1",
doi = "10.1007/s00025-020-01264-7",
language = "English (US)",
volume = "75",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Birkhauser Verlag Basel",
number = "4",
}