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 ${\pi }_i(X;\mathbb{Z})$ are the usual homotopy groups of X.