A "q-deformed" generalization of the Hosszu-Gluskin theorem

In this paper a new form of the Hossz\'u-Gluskin theorem is presented in terms of polyadic powers and using the language of diagrams. It is shown that the Hossz\'u-Gluskin chain formula is not unique and can be generalized ("deformed") using a parameter q which takes special integer values. A version of the "q-deformed" analog of the Hossz\'u-Gluskin theorem in the form of an invariance is formulated, and some examples are considered. The "q-deformed" homomorphism theorem is also given.