On Post-Gluskin-Hosszu Theorem

The Post-Gluskin-Hosszu Theorem(also called Gluskin-Hosszu or Hosszu-Gluskin Theorem) refers to an n-ary grouphA; ( )i and a bi- nary group hA; -i, deflned on the same set A. E. Post stated and proved this Theorem, while considering instead of the group hA; -i, the isomor- phic to it associated group A0. This reveals Post's basic contribution, and justifles the inclusion of his name as leading co-author of the Theorem. Apparently, M. Hosszu was not aware of Post's result, while L.M. Gluskin did not directly address n-ary groupsin his research, focusing mainly on a large class on algebraic systems ( positional operatives), for which he obtained a series of notable results, out of these, one of the consequences being exactly the Post-Gluskin-Hosszu Theorem.