In topology, a branch of mathematics, for i ≥ 2 {\displaystyle 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 ) {\displaystyle (G,i)} to X, and is denoted by π i ( X ; G ) {\displaystyle \pi _{i}(X;G)} . For i ≥ 3 {\displaystyle i\geq 3} , π i ( X ; G ) {\displaystyle \pi _{i}(X;G)} is a group. The groups π i ( X ; Z ) {\displaystyle \pi _{i}(X;\mathbb {Z} )} are the usual homotopy groups of X.
References
Weibel, Charles (2013). "The K-book: An introduction to algebraic K-theory".