Decompositions of good involutions on quandles

Yasuhito Nakajima; Kentaro Yamaguchi

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arXiv · 2608.19951

Decompositions of good involutions on quandles

Yasuhito Nakajima·Kentaro Yamaguchi

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Abstract

We study the behavior of good involutions under two fundamental constructions of quandles: interaction-free unions and direct products. In particular, we show that the set of good involutions on a quandle decomposes naturally into the set of involutions on its maximal trivial component and the set of good involutions on the complement. Moreover, we construct an example of a connected noninvolutory symmetric quandle with multiple good involutions, which serves as a counterexample to a conjecture by Ta.

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Yasuhito Nakajima, Kentaro Yamaguchi. 2026-08-20. Decompositions of good involutions on quandles. https://arxiv.org/abs/2608.19951

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