Binary operations for homotopy groups with coefficients

We define and study binary operations for homotopy groups with coefficients, and give conditions to prove that certain binary operations are the homomorphic image of the generalized Whitehead product. This allows carrying over properties of the generalized Whitehead product to these operations. We discuss two classes of binary operations, i.e., the Whitehead products and the torsion products. We also introduce a new class of operations called Ext operations and determine some of its properties. Then we compare the torsion product to the Whitehead product in a special case, and prove that the smash product of two Moore spaces has the homotopy type of a wedge of two Moore spaces.