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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Coherent group rings and finiteness conditions for CW-complexes


Author: Philip S. Hirschhorn
Journal: Proc. Amer. Math. Soc. 74 (1979), 368-370
MSC: Primary 55P99; Secondary 16A27
MathSciNet review: 524319
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0524319-8
PII: S 0002-9939(1979)0524319-8
Article copyright: © Copyright 1979 American Mathematical Society