Homotopy group with coefficients

In topology, a branch of mathematics, for $$i \ge 2$$, 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 $$(G, i)$$ to X, and is denoted by $$\pi_i(X; G)$$. For $$i \ge 3$$, $$\pi_i(X; G)$$ is a group. The groups $$\pi_i(X; \Z)$$ are the usual homotopy groups of X.