Remark on homomorphisms of groups - Gusić, Ivica (Annales Mathematicae Silesianae, 2022)
Assume that (X,+) are commutative groups, and C is a subset of X fulfilling the conditions C+C ⊆ C and C-C = X. A function f: X→Y is called C-additive function if it satisfies functional equation f(x+y) = f(x) + fy), for all x,y∈X such that y-x∈C∪(-C)∪0. In [1, Theorem 8.4] has been proved that every C-additive function f: X→Y is additive. In the proof the comutativity has been essentially used. Here we present a simple proof of an analogous statement in the case of arbitrary groups.