Three approaches to the notion of functions maximally differing from homomorphisms

We consider three approaches to the notion of functions (mappings) from a finite group into a finite group which are maximally differing from homomorphisms. These approaches are based on the notion “functions closeness” which is an alternative to the notion “Hamming distance between functions”. The notions of absolute nonhomomorphity of the function, minimal closeness of function to homomorphisms and of bent-function are generalized and studied.