On Post–Gluskin–Hosszu theorem

Post–Gluskin–Hosszu theorem is known as Gluskin-Hosszu or Hosszu–Gluskin theorem. In the formulation of this theorem there is an $n$-ary group $< A, [\,] >$ and some binary group $< A,\circ >$. These groups have a common carrier $A$. E. Post formulated and proved this theorem considering isomorphous copy of $A_0$ (associated group) instead of group $< A,\circ >$. In our opinion the absence of the name of E. Post in the title of the theorem is an embarrassing mistake which must be corrected. Apparently, M. Hosszu didn’t know anything about the results of E. Post. It is necessary to note that L. M. Gluskin was not engaged in the study of $n$-ary groups. He investigated a large class of algebraic systems — positional operatives, and achieved a series of important results. Post–Gluskin–Hosszu theorem is among numerous consequences of these results.