Abstract

1. The F^G-construction gives a special simplicial group model for the loops on K(Z/p^r,1) smash X. A certain natural filtration will be considered.

2. We define certain functors from the category of simplicial Hopf algebras to the category of algebras. By using simplicial group rings, the group ring of the homotopy groups of K(Z/p^r,1) smash X are shown to be given by these functors on certain special simplicial Hopf algebras.

3. Certain specific combinatorial descriptions of the homotopy groups of the suspension of K(Z/p^r,1).