Homotopy group with coefficients

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In topology, a branch of mathematics, for $i\geq 2$ , 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 $\pi _{i}(X;G)$ .^[1] For $i\geq 3$ , $\pi _{i}(X;G)$ is a group. The groups $\pi _{i}(X;\mathbb {Z} )$ are the usual homotopy groups of X.