A new protomodular analog of the classical criterion for the existence of a group term in the algebraic theory of a variety of universal algebras is given. To this end, the notion of a right-cancellable protomodular algebra is introduced. The translation group functor from the category of right-cancellable algebras of a protomodular variety to the category of groups is constructed. It is proved that the algebraic theory of a variety of universal algebras contains a group term if and only if it contains protomodular terms with respect to which all algebras from the variety are right-cancellable. Moreover, the right-cancellable algebras from the simplest protomodular varieties are characterized as sets with principal group actions as well as groups with simple additional structures.

给出了各种泛代数的代数理论中群项存在的经典判据的一种新的原型模模拟。为此，引入了右可消原模代数的概念。构造了从原模变体的右可消代数范畴到群范畴的翻译群函子。证明了泛泛代数的代数理论包含一个群项当且仅当它包含原模项，关于该原模项，所有来自泛代数的代数都可以右可消。此外，来自最简单原模变体的右可取消代数被表征为具有主群作用的集合以及具有简单附加结构的群。