After introducing the concept of algebraic projective relation of abstract homogeneous systems, we consider the projectivity of normal left subloops of homogeneous left loops. We introduce the concept of Akivis left loops on abstract groups, and show that any normal subgroup H of an abstract group G induces a normal left subloop of each Akivis left loop on G, which is in projective relation with H, and that Akivis left loops of the quotient group G/H are equal to quotient homogeneous left loops of Akivis left loops.