Commutator theory for racks and quandles

We adapt the commutator theory of universal algebra to particular setting racks and quandles, exploiting a Galois connection between congruences certain normal subgroups displacement group. Congruence properties, such as abelianness centrality, are reflected by corresponding relative groups, global solvability nilpotence, properties whole To show new tool in action, we present three applications: non-existence theorems for quandles (no connected involutory order $2^k$, no latin $\equiv2\pmod4$), non-colorability theorem (knots with trivial Alexander polynomial not colorable solvable quandles; particular, finite quandles), strengthening Glauberman's results on Bruck loops odd order.