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arXiv · 2609.17438

Quandles associated with group actions

Ryoya Kai
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Abstract

A quandle is an algebraic system that can be regarded as a generalization of the conjugation operation in groups. In this paper, we establish a Cayley-type embedding theorem for finite quandles. To this end, we study a quandle construction associated with group actions and determine its fundamental structural properties. Applying the construction to the natural action of the symmetric group, we obtain a quandle into which every quandle of cardinality $n$ embeds.

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BibTeXRIS

Ryoya Kai. 2026-09-16. Quandles associated with group actions. https://arxiv.org/abs/2609.17438

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