Hom(A, G), II. Original Research Article

In this paper, we prove that for any finite groups A and G, the number of homomorphisms from A to G is divisible by the greatest common divisor of ((A/A′) : Φ(A/A′)) and G, where A′ is the commutator subgroup of A and Φ(A/A′) is the Frattini subgroup of A/A′.