Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 203-218 MSC: Primary 20N99. DOI: 10.4064/fm715-12-2019 Published online: 27 March 2020
We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. By determining when two biquandle structures yield isomorphic biquandles, we obtain a relationship between the automorphism group of a biquandle and the automorphism group of its underlying quandle. As an application, we determine the automorphism groups of Alexander and dihedral biquandles. We also discuss product biquandles and describe their automorphism groups.