On generalized quandle extensions of a quandle defined on a group

In 1980s, Joyce and Matveev introduced a quandle which is an algebraic structure related to knot theory. In the papers, they also showed that for given a group and a group automorphism, there is a quandle structure on the group, later called ’generalized Alexander quandle’. In particular, when the automorphism is an inner automorphism by a fixed element $\zeta$, we denote the quandle operation by $\triangleleft_{\zeta}$. In this talk, we study a relationship between group extensions of a group $G$ and quandle extensions of a generalized Alexander quandle $(G,\triangleleft_{\zeta})$ whose underlying set coincides with that of $G$. This is a joint work with Y.Bae and S.Carter.