Functions with variative-coordinate polynomiality over group

A class of VCP-functions, that is, of functions with the variative-coordinate polynomiality over group, is defined. It is an extension of the class of VCP-functions over primary ring of residues. An algorithm for finding coordinates for group elements is presented. It is shown that the class of VCP-functions over $UT_n(\mathbb Z_p)$ does not coincide with the class of polynomial function. A formula for constructing the inverse of a bijective VCP-function over $UT_n(\mathbb Z_p)$ is proposed.