A note on generalized equivariant homotopy groups

In this paper, we generalize the equivariant homotopy groups or equivalently the Rhodes groups. We establish a short exact sequence relating the generalized Rhodes groups and the generalized Fox homotopy groups and we introduce $\mathrm{\Gamma }$-Rhodes groups, where $\mathrm{\Gamma }$ admits a certain co-grouplike structure. Evaluation subgroups of $\mathrm{\Gamma }$-Rhodes groups are discussed.