Nilpotent left quasigroups

TL;DR

This paper explores the structure of nilpotent left quasigroups, extending known results from quandles to a broader class, and investigates their central congruences and algebraic properties.

Contribution

It extends characterizations of finite nilpotent latin quandles and distributive varieties from quandles to idempotent left quasigroups.

Findings

Extended characterization of finite nilpotent latin quandles.

Generalized distributive varieties to idempotent left quasigroups.

Analyzed central congruences in left quasigroups.

Abstract

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 can extend the characterization of finite nilpotent latin quandles and the characterization of distributive varieties of quandles to the setting of idempotent left quasigroups.