Unstable ₁-periodic homotopy groups of a Moore space

The mod p vi -periodic homotopy groups of a space X are defined by considering the homotopy classes of maps of a Moore space into X and then inverting the Adams self-map of a Moore space. In this paper the modp V\ -periodic homotopy groups of a Moore space are computed by using the Cohen-Moore-Neisendorfer splitting of the space of loops on a Moore space. The Adams map is shown to be compatible with this splitting and it is proved that the homomorphism of vi-periodic homotopy groups induced by the Adams map is an isomorphism.