Homotopy group with coefficients

In topology, a branch of mathematics, for i ≥ 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 π i ( X ; G ) . For i ≥ 3 , π i ( X ; G ) is a group. Note π i ( X ; Z ) are the usual homotopy groups of X.