Equivalents for a quasivariety to be generated by a single structure (Q1005982)

In \textit{A. I. Mal'tsev}'s article [Algebra Logika 5, No. 3, 3--9 (1966; Zbl 0248.08006)], there can be found a condition for a quasivariety to be generated by a single structure, namely, the embedding property for nontrivial structures, which states that if \(A,B\in \mathcal{K}\) are nontrivial, then there exists \(C\in \mathcal{K}\) such that \(A,B\) are embeddable into \(C.\) In this paper, the authors present more equivalent conditions for a quasivariety of structures to be generated by a single structure, thus equivalent to Mal'tsev's condition.