A “q-Deformed” Generalization Of The Hosszu-Gluskin Theorem

Abstract

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