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In an earlier paper, the authors proved that a process describedmuch earlier for passing from a finitely generated nilpotent groupN of a certain kind to a nilpotent space X of finite type produced a bijection of Mislin genera (N)≅(X). The present paper is concerned with relatedresults obtained by weakening the restrictions on N andgeneralizing the homotopical nature of the spaces X to beassociated with a given N

On the Mislin genus of certain circle bundles and noncancellation