Compatible structures of generalized Alexander quandles: distributivity and medial identities

A. N. Borodin^a, M. V. Neshchadim^b, A. A. Simonov<sup>c

a</sup> Gorno-Altaisk State University, Gorno-Altaisk, Russia
^b Sobolev Institute of Mathematics, Novosibirsk, Russia
^c Novosibirsk State University, Novosibirsk, Russia

Abstract: We study the following question: under what conditions does a group admit two generalized Alexander quandle structures that are compatible with each other via the identity of right distributivity or the generalized medial identity?

Keywords: quandle, generalized Alexander quandle, right distributivity, generalized medial identity, compatible identities, group, automorphism.

UDC: 512.548+515.162.8

MSC: 35R30

Received: 17.02.2025
Revised: 02.05.2025
Accepted: 13.05.2025

DOI: 10.33048/smzh.2025.66.403

 English version: Siberian Mathematical Journal, 2025, 66:4, 903–913