On \(\tau\)-closed formations of \(n\)-ary groups (Q2754821)

Recall that an algebraic system \(\langle G,(\cdot)\rangle\) with an \(n\)-ary operation \((\cdot)\) is called \(n\)-ary group if this operation is associative and each of the two equations \((xa_1\dots a_{n-1})=a\), \((a_1\dots a_{n-1}y)=a\) can be solved in \(G\). Analogously to groups one can define formations of \(n\)-ary groups. Wider is the notion of a semi-formation: it is a class of \(n\)-ary groups which is closed relative to homomorphic images (congruences) of its elements. The author studies \(\tau\)-closed semi-formations of \(n\)-ary groups (which are generated by the so-called subgroup functor \(\tau\)). All results (7 theorems) are given without proofs.