19 citations · 50 across the 15 of their papers we have counts for
23 papers
On Simply Connected Quandles
Marco Bonatto
In this paper we provide an alternative characterization of finite simply connected quandles involving only cocycles with values in abelian groups of prime size. As a corollary of…
Nilpotent left quasigroups
Marco Bonatto
In this paper we investigate central congruence of left quasigroups in the sense of Freese and McKenzie \cite{comm} and we extend some known results for quandles. In particular, we…
Groups with cofinite Zariski topology and potential density
Marco Bonatto, Dikran Dikranjan, Daniele Toller
Tkachenko and Yaschenko [34] characterized the abelian groups G such that all proper unconditionally closed subsets of G are finite, these are precisely the abelian groups G having…
Central nilpotency of skew braces
Marco Bonatto, Přemysl Jedlička
Skew braces are algebraic structures related to the solutions of the set-theoretic quantum Yang-Baxter equation. We develop the central nilpotency theory for such algebraic structu…
On the axioms of singquandles
Marco Bonatto, Alessia Cattabriga
In this paper we deal with the notion of singquandles introduced in Indu R. U. Churchill, Mohamed Elhamdadi, Mustafa Hajij, and Sam Nelson, Singular knots and involutive quandles,…
Superconnected left quasigroups and involutory quandles
Marco Bonatto
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 \cite{Maltsev_paper…
Knot quandle decomposition along a torus
Marco Bonatto, Alessia Cattabriga, Eva Horvat
We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle…
Medial and semimedial left quasigroups
Marco Bonatto
In this paper we investigate the class of semimedial left quasigroups, a class that properly contains racks and medial left quasigroups. We extend most of the results about commuta…
Quandles with orbit series conditions
Marco Bonatto, Alissa S. Crans, Timur Nasybullov +1
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, th…
Mal'cev classes of left-quasigroups and Quandles
Marco Bonatto, Stefano Fioravanti
In this paper we investigate some Mal'cev classes of varieties of left-quasigroups. We prove that the weakest Mal'cev condition for a variety of left-quasigroup is having a Mal'cev…
Skew braces of size I: abelian type
E. Acri, M. Bonatto
This is the first part of a series of two articles. In this paper we enumerate and classify the left braces of size where and are distinct prime numbers by the class…
Skew braces of size II: non-abelian type
E. Acri, M. Bonatto
In this paper we enumerate the skew braces of non-abelian type of size for primes with by the classification of regular subgroups of the holomorph of the non-abe…
Skew braces of size
Emiliano Acri, Marco Bonatto
In this paper we enumerate the skew braces of size for odd primes by the classification of regular subgroups of the holomorph of the groups of size . In particul…
Involutive latin solutions of the Yang-Baxter equation
Marco Bonatto, Michael Kinyon, David Stanovský +1
Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all…
A Universal algebraic approach to rack coverings
Marco Bonatto, David Stanovský
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abst…
Skew braces of size
E. Acri, M. Bonatto
We construct all skew braces of size (where are primes) by using Byott's classification of Hopf--Galois extensions of the same degree. For there…
Connected quandles of size and
Marco Bonatto
We classify all non-simple connected quandles of size and where are primes, as a special family of locally strictly simple quandles (i.e. quandles for which all pro…
On connected quandles of prime power order
Giuliano Bianco, Marco Bonatto
We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size for , using a combination of group th…
Principal and Doubly Homogeneous Quandles
Marco Bonatto
In the paper we describe the class of principal quandles and show that connected quandles can be decomposed as a disjoint union of principal quandles. We also prove that simple aff…
Commutator theory for racks and quandles
Marco Bonatto, David Stanovský
We adapt the commutator theory of universal algebra to the particular setting of racks and quandles, exploiting a Galois connection between congruences and certain normal subgroups…
On the Structure of Hom Quandles
Marco Bonatto, Alissa S. Crans, Glen T. Whitney
We continue the study of the quandle of homomorphisms into a medial quandle begun in Crans and Nelson. We show that it suffices to consider only medial source quandles, and therefo…
Generalize Heisenberg Groups and Self-Duality
Marco Bonatto, Dikran Dikranjan
This paper compares two generalizations of Heisenberg groups and studies their connection to one of the major open problems in the field of locally compact abelian groups, namely t…
Simply connected latin quandles
Marco Bonatto, Petr Vojtěchovský
A (left) quandle is connected if its left multiplication group acts transitively. In 2014, Eisermann introduced the concept of quandle coverings, corresponding to so-called constan…