A normal subgroup Hof a group G is said to be a direct factor (direct summand if G is additive abelian) if there exists a (normal) subgroup K of G such that G = H X K.

(a) If H is a direct factor of K and K is a direct factor of G, then H is normal in G.

(b) If H is a direct factor of G, then every homomorphism H → G may be extended to an endomorphism G → G. However, a monomorphism H → G need not be extendible to an automorphism G → G.