16 papers · 1 filter
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…
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…
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…