Group homomorphisms hi such that h1(x1)+cdots, three dots, centered+hn(xn)=y is solvable Original Research Article

We describe a class of group homomorphisms hi:Xi→Y, with Y abelian, such that the solvability of h1(x1)+cdots, three dots, centered+hn(xn)=y can be characterized and the solution set can be completely described. We apply our result to the matrix equation A1X1B1+cdots, three dots, centered+AnXnBn=C.