On connection between reducibility of an n-ary quasigroup and that of its retracts

Denis Krotov, Vladimir Potapov

An $n$-ary operation $Q:S^n\to S$ is called an $n$-ary quasigroup of order $|S|$ if in the equation $x_0=Q(x_1,...,x_n)$ knowledge of any $n$ elements of $x_0,...,x_n$ uniquely spe…