Coherent group rings and finiteness conditions for CW-complexes

Hirschhorn, Philip S.

doi:10.1090/S0002-9939-1979-0524319-8

Coherent group rings and finiteness conditions for CW-complexes
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by Philip S. Hirschhorn PDF

Proc. Amer. Math. Soc. 74 (1979), 368-370 Request permission

Abstract:

We characterize the class of groups G that have the property that if X is any space for which ${\pi _1}X \cong G$, then X is homotopy equivalent to a space with finite skeleta in the “stable range” if and only if the homotopy groups of X are finitely presented $Z[G]$-modules in this range. This class of groups includes all finite groups, finitely generated abelian groups, finitely generated nilpotent groups, finitely generated free groups, and free products of any of these.

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Simplicial spaces, nuclei, and m-groups

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