Various constructions of generalized Alexander quandles are studied. It is proved that, up to isomorphism, they reduce to two types. Conditions are found under which such quandles are abelian. A construction of an extension of a generalized Alexander quandle to the direct product of two groups is given. Conditions for constructing a quandle over a module and a near-ring are found.
Borodin et al. (Thu,) studied this question.