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The associated graded ring of an integral group ring

Published online by Cambridge University Press:  24 October 2008

Inder Bir S. Passi  and
Lekh Raj Vermani
Inder Bir S. Passi
Affiliation:
B. N. Chakravarty University, Kurukshetra, India
Lekh Raj Vermani
Affiliation:
B. N. Chakravarty University, Kurukshetra, India
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Extract

Let G be an Abelian group, the symmetric algebra of G and the associated graded ring of the integral group ring ZG, where (AG denotes the augmentation ideal of ZG). Then there is a natural epimorphism (4)

which is given on the nth component by

In general θ is not an isomorphism. In fact Bachmann and Grünenfelder(1) have shown that for finite Abelian G, θ is an isomorphism if and only if G is cyclic. Thus it is of interest to investigate ker θn for finite Abelian groups. In view of proposition 3.25 of (3) it is enough to consider finite Abelian p-groups.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 1 , July 1977 , pp. 25 - 33
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

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