Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T13:10:17.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Natural maps of extension functors and a theorem of R. G. Swan

Published online by Cambridge University Press:  24 October 2008

P. J. Hilton  and
D. Rees
P. J. Hilton
Affiliation:
Birmingham University
D. Rees
Affiliation:
Exeter University
Get access Rights & Permissions [Opens in a new window]

Extract

The present paper has been inspired by a theorem of Swan(5). The theorem can be described as follows. Let G be a finite group and let Γ be its integral group ring. We shall denote by Z an infinite cyclic additive group considered as a left Γ-module by defining gm = m for all g in G and m in Z. By a Tate resolution of Z is meant an exact sequence

where Xn is a projective module for − ∞ < n < + ∞, and

.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 489 - 502
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Buchsbaum, D. A.Exact categories and duality. Trans. Amer. Math. Soc. 80 (1955), 1–34.Google Scholar
(2)Cartan, H. and Eilenberg, S.Homological algebra (Princeton, 1956).Google Scholar
(3)Cartier, P.Les Groupes Ext8 (A, B). Exposé 3, Séminaire A. Grothendieck, Paris (1957) (mimeographed).Google Scholar
(4)Hilton, P. J.Homolopy theory of modules and duality. Symposium internacional de Topologia Algebraica, 1958, pp. 273–81.Google Scholar
(5)Swan, R. G.Periodic resolutions for finite groups. Ann. Math. 72 (1960), 267–92.CrossRefGoogle Scholar