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Abstract

Let G be a finite group, $\mathbb{O}_G$ the category of canonical orbits of G and $A : \mathbb{O}_G → \mathbb{A}$b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with $Ext^{n-1}(A, A ⊗ A)$. Then the case $G = ℤ_{p^k}$ leads to an example of infinitely many G-homotopically distinct G-maps $φ_i : X → Y$ such that $φ_i^H$, $φ_j^H : X^H → Y^H$ are homotopic for all i,j and all subgroups H ⊆ G.