Associated groups of symmetric quandles

Toshiyuki Akita; Kakeru Shikata

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arXiv · 2505.23507

Associated groups of symmetric quandles

Toshiyuki Akita·Kakeru Shikata

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Abstract

In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a group-theoretic characterization of associated groups of symmetric quandles. Furthermore, we show that a symmetric quandle is embeddable if and only if its underlying quandle is embeddable, and we determine the abelianization of these associated groups.

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Toshiyuki Akita, Kakeru Shikata. 2025-05-29. Associated groups of symmetric quandles. https://arxiv.org/abs/2505.23507

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