Right-cancellable protomodular algebras (Q2073372)

In this paper, the author introduces a new protomodular analog of the classical criterion for the existence of a group term in the algebraic theory of a group term in the algebraic theory of a variety of universal algebras. The algebraic theory of a variety of universal algebras contains a group term if and only if it contains a 0-ary term and an associative Mal'cev term. In a previous paper [Algebra Univers. 81, No. 1, Paper No. 1, 12 p. (2020; Zbl 07146745)], the author gave a protomodular analog of the above mentioned criterion for the existence of a group term in a variety of universal algebras. In this paper, the author gives another criterion for the existence of a group term in a variety of universal algebras. In Section 5, group operations on right-cancellable protomodular algebras, the author shows that right-cancellable $v_n$-algebras can be characterized as groups with simple additional structures.