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