Abstract: In this paper, we introduce and study classes of triangular and near-trivial quandles. We characterize these classes in terms of inner automorphisms. We prove that 1. every triangular quandle is almost trivial; 2. the class of near-trivial quandles is an algebraic variety; 3. the class of triangular quandles is not closed under taking Cartesian products. We find necessary and sufficient conditions under which a generalized Alexander quandle is near-trivial or triangular. We also consider the questions of extension and constructive construction of such quandles. In particular, we present an algorithm that allows us to construct all triangular quandles on a finite set of elements. The work was supported by the Fundamental Research Program of the Siberian Branch of the Russian Academy of Sciences (no. I.1.5, Project FWNF 2022-0009). Borodin A.N., Neshchadim M.V. and Simonov A.A. Triangular and near-trivial quandles. Submitted to the journal Algebra and logic.

Cite: Neshchadim M.V. , Borodin A.N. , Simonov A.A.
Triangular and near-trivial quandles
6 INTERNATIONAL CONFERENCE GROUPS AND QUANDLES IN LOW-DIMENSIONAL TOPOLOGY 10-11 Jun 2025