  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. 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.
This, in particular, gives a partial answer to the extended version of an open
problem from loop theory whether any Hausdorff topological (semi-)loop is
completely regular. 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.
