# Homotopy group with coefficients

## From Wikipedia, the free encyclopedia

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*.