Homotopy representations and spheres of representations (Q1077021)

Let V(G) be the group of homotopy representations of the finite group G introduced by the reviewer and \textit{T. Petrie} [Publ. Math., Inst. Haut. Étud. Sci. 56, 129-170 (1982; Zbl 0507.57025)] and let V(G,l)\(\subset V(G)\) be the subgroup represented by linear representations. The author shows that \(V(G,l)=V(G)\) if and only if G is cyclic or a dihedral 2- group. A similar result is shown for the Picard group of the Burnside ring provided G is assumed nilpotent.