Superconnected left quasigroups and involutory quandles

Abstract

In this paper we study the classes of superconnected and superfaithful left quasigroups, that are relevant in the study of Mal’cev varieties of left quasigroups. Then we focus on quandles and in particular to the involutory ones. We extend the main result of [a paper by Erofeeva] to the infinite case and we offer a characterization of several classes of involutory quandles in terms of the properties of the canonical generators of the displacement group, improving the main results of [a paper by Nobusawa].

Keywords:

• Involutory quandles
• left quasigroup
• quandles

2020 Mathematics Subject Classification:

• 20N02
• 16T25
• 57M27

Acknowledgments

The author is grateful to Prof. Gastón García for the fruitful discussion in La Plata around the notion of superconnected quandle and related problems. The author would also like to thank Prof. David Stanovský for pointing him out the relevant paper [24].