Homotopy group with coefficients

In topology, a branch of mathematics, for formula_1, the "i"-th homotopy group with coefficients in an abelian group "G" of a based space "X" is the pointed set of homotopy classes of based maps from the Moore space of type formula_2 to "X", and is denoted by formula_3. For formula_4, formula_3 is a group. The groups formula_6 are the usual homotopy groups of "X".