19 citations · 50 across the 15 of their papers we have counts for
8 papers · 1 filter
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…