Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

A quandle is an algebraic system originating in knot theory, which can be regarded as a generalization of the operation of conjugation of groups. This structure naturally defines two subgroups of its automorphism group, which are called the inner automorphism group and the displacement group, and they act on the quandle from the right. For a quandle with such groups being finitely generated, we investigate the graph structures induced from the actions, and the corresponding metric spaces. The graph structures are defined by the notion of the Schreier graph, which is a natural generalization of the Cayley graph for a group. In particular, the metric associated with the displacement group of an important class of quandles, namely, generalized Alexander quandles, had been studied in detail. We show that this metric space is quasi-isometric to the displacement group equipped with a word metric. Finally, we provide some examples that are quasi-isometric to typical metric spaces.

DOI： 10.1142/s0129167x26500539

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/91339133

Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.topol.2025.109576

Publishing type：Research paper (scientific journal)   Publisher：Mathematical Sciences Publishers  

DOI： 10.2140/pjm.2024.333.309

Publishing type：Research paper (scientific journal)  

DOI： 10.4171/ggd/841