6 papers
Latin quandles of size
Marco Bonatto, Filippo Spaggiari
In this paper we obtain the classification of latin quandles of size where is an odd prime. In particular we have that such quandles are always subdirectly reducible but…
On Core Quandles
Filippo Spaggiari, Marco Bonatto
We characterize several properties of core quandles in terms of the properties of their underlying groups. Specifically, we characterize connected cores providing an answer to an o…
Involutive (simple) latin solutions of the Yang-Baxter equation and related (left) quasigroups
Marco Bonatto, Marco Castelli
In this paper, we study involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with regular displacement group. In particular, we completely describe the blo…
A conjecture on superconnected quandles
Marco Bonatto
We study simple superfaithful and superconnected quandles and we found counterexamples to a conjecture suggested by computational data. We provide also examples of superconnected q…
Oriented singquandles and related algebraic structures
Marco Bonatto
In this paper we consider the algebraic structures related to invariants of topological structures introduced respectively in [CEKL22] and [ADEM19]. Our main results is to show how…
Two Galois connections for left quasigroups
Marco Bonatto
We investigate two Galois connection between the congruence lattice and the lattice of subgroups of the displacement group of left quasigroups. Such connections were already studie…