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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
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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

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References

REFERENCES

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(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