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arXiv · 2609.17438

Quandles from group actions and a Cayley-type embedding theorem

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. We study a quandle construction associated with group actions and determine its structural properties, including its inner automorphism group, connected components, and subquandles. As a principal application, we establish a Cayley-type embedding theorem for finite quandles. Applying the construction to the natural action of the symmetric group, we obtain, for each $n$, a single quandle into which every quandle of cardinality $n$ embeds.

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BibTeXRIS

Ryoya Kai. 2026-09-22. Quandles from group actions and a Cayley-type embedding theorem. https://arxiv.org/abs/2609.17438

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