Constructions of Quandles over Groups and Rings

We present the following constructions: extension of a trivial quandleby a group with a nontrivial abelian subgroup,a quandle over a noncommutative groupby an arbitrary antiautomorphism,a quandle presenting from a generalized Alexander quandlewith the replacement of the automorphism by a central antiautomorphism, anda quandle over an  $ n $ -dimensional moduledepending on  $ n(n-1)-1 $ parameters with $ n\geq 2 $ in a commutative unital ring.