Title: Automorphism groups of quandles and related groups,
Abstract: In this paper we study different questions concerning automorphisms of
quandles. For a conjugation quandle $Q={\rm Conj}(G)$ of a group $G$ we
determine several subgroups of ${\rm Aut}(Q)$ and find necessary and sufficient
conditions when these subgroups coincide with the whole group ${\rm Aut}(Q)$.
In particular, we prove that ${\rm Aut}({\rm Conj}(G))={\rm Z}(G)\rtimes {\rm
Aut}(G)$ if and only if either ${\rm Z}(G)=1$ or $G$ is one of the groups
$\mathbb{Z}_2$, $\mathbb{Z}_2^2$ or $\mathbb{Z}_3$. For a big list of Takasaki
quandles $T(G)$ of an abelian group $G$ with $2$-torsion we prove that the
group of inner automorphisms ${\rm Inn}(T(G))$ is a Coxeter group. We study
automorphisms of certain extensions of quandles and determine some interesting
subgroups of the automorphism groups of these quandles. Also we classify finite
quandles $Q$ with $3\leq k$-transitive action of ${\rm Aut}(Q)$.