Homotopy group with coefficients

Summary

A homotopy group with coefficients in $\Z/k$ is the set of homotopy classes of maps from a mod $k$ Moore space into a space. It plays the role for homotopy groups that homology with coefficients plays for homology. These groups sit in a short exact sequence with the ordinary homotopy groups and are used to study $p$-primary phenomena in homotopy theory.