Mal'cev classes of left-quasigroups and Quandles

Superconnected left quasigroups and involutory quandles

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}. Then we focus on quandles and in particular to the involutory ones. We extend the main result of \cite{involutive_quandles_russo} to the infinite case and we offer a characterization of several classes of involutory quandles in terms of the properties of the canonical generators of the displacement group, improving the main results of \cite{Nobu}.

Medial and semimedial left quasigroups

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 commutator theory for racks collected in \cite{CP} and some of the results concerning Malt'sev conditions for quandles collected in \cite{Maltsev_paper} to the class of semimedial left quasigroups.

On rectifiable spaces and its algebraical equivalents, topological algebraic systems and Mal'cev algebras

We investigate the rectifiable spaces, the Mal'cev algebras, the almost quasivarieties of topological algebraic systems and their free systems and others. It specifies and corrects the roughest mistakes, incorrect statements and nonsense of the introduced concepts connected with the concepts listed before, which are available in numerous papers on topological algebraic systems, basically in papers of Academician Choban M.M. and his disciples.

pro-p群的连续Mal'cev Qp完备化

Continuous Mal'cev Qp-Completion of Pro-p Groups

本文针对拓扑有限生成pro-p群，利用Tannakian形式论、Hopf代数和p进解析群三种方式构造其连续Mal'cev Qp完备化，并研究该完备化的相关性质。

Grün引理在半结合Mal'cev代数上的推广

Grün's Lemma for Semiassociative Mal'cev Algebras

本文将Grün引理从斜辫子推广到半结合Mal'cev代数，刻画了完美代数上中心列在第二中心稳定的条件，并利用换位子生成集描述完成证明。

Nilpotency and strong nilpotency for finite semigroups

Nilpotent semigroups in the sense of Mal'cev are defined by semigroup identities. Finite nilpotent semigroups constitute a pseudovariety, $\mathsf{MN}$, which has finite rank. The semigroup identities that define nilpotent semigroups, lead us to define strongly Mal'cev nilpotent semigroups. Finite strongly Mal'cev nilpotent semigroups constitute a non-finite rank pseudovariety, $\mathsf{SMN}$. The pseudovariety $\mathsf{SMN}$ is strictly contained in the pseudovariety $\mathsf{MN}$ but all finite nilpotent groups are in $\mathsf{SMN}$. We show that the pseudovariety $\mathsf{MN}$ is the inters…