Automorphisms and antiautomorphisms of quandles

In this paper we provide the conditions under which an automorphism or an antiautomorphism of a group $G$ induces an automorphism or an antiautomorphism of the $m$-conjugation quandle $\operatorname{Conj_{m}}(G),\,\, m\in \mathbb{Z}$, the core quandle $\operatorname{Core}(G)$, the generalized Alexander quandle $\operatorname{Alex}(G,\phi)$ where $\phi\in \operatorname{Aut}(G)$ and some others. We also construct automorphisms of these quandles that do not originate from $G$.