| Abstract: | Let G be a group, let A be an Abelian group, and let n be an integer such that n  –1. In the paper, the sets 
n
(G,A) of functions from G into A of degree not greater than n are studied. In essence, these sets were introduced by Logachev, Sal'nikov, and Yashchenko. We describe all cases in which any function from G into A is of bounded (or not necessarily bounded) finite degree. Moreover, it is shown that if G is finite, then the study of the set
n
(G,A) is reduced to that of the set n(G/O
p
(G),A
p
) for primes p dividing  G/G . Here O
p
(G) stands for the p-coradical of the group G, A
p
for the p-component of A, and G for the commutator subgroup of G. |
