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  "body": "\n## Summary\n\nA homotopy group with coefficients in $\\Z/k$ is the set of homotopy classes of maps from a mod $k$ [[Moore space|68MA0RM5P6]] into a space.\nIt plays the role for [[homotopy groups|P976WYEFMB]] that homology with coefficients plays for homology.\nThese groups sit in a short exact sequence with the ordinary homotopy groups and are used to study $p$-primary phenomena in homotopy theory.\n\n## Explanations\n\n### L1 human\n\nAn ordinary homotopy group records maps from a sphere into a space.\nA homotopy group with coefficients replaces the sphere by a space that is a sphere with a disk glued on by a degree $k$ map.\nMaps from that space see the parts of homotopy that are killed by $k$ and the classes modulo $k$.\nFor example, for the sphere $S^n$ with $n \\ge 3$, the group $\\pi_n(S^n; \\Z/k)$ is cyclic of order $k$.\n",
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