English

Associated groups of symmetric quandles

Geometric Topology 2025-08-12 v4 Group Theory

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.

Keywords

Cite

@article{arxiv.2505.23507,
  title  = {Associated groups of symmetric quandles},
  author = {Toshiyuki Akita and Kakeru Shikata},
  journal= {arXiv preprint arXiv:2505.23507},
  year   = {2025}
}

Comments

Introduction was rewritten and several results were added