Passi, Inder Bir S. ; Vermani, Lekh Raj
(1977)
*The associated graded ring of an integral group ring*
Mathematical Proceedings of the Cambridge Philosophical Society, 82
(1).
pp. 25-33.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0305004100053640

## Abstract

Let G be an Abelian group, S(G)=∑_{n≥0}SP^{n}(G) the symmetric algebra of G and grZG=∑_{n≥0}Q_{n}(G) the associated graded ring of the integral group ring ZG, where Q_{n}(G)=A_{G}^{N}/A_{G}^{n+1}(A_{G} (A_{G} denotes the augmentation ideal of ZG). Then there is a natural epimorphism (4) θ (G): S(G) → grZG which is given on the nth component by θ_{n}(x_{1}⊗^....⊗^x_{n}=(x_{n}-1)....(x_{n}-1)+A_{G}^{n+1} (x_{n}εG). In general θ is not an isomorphism. In fact Bachmann and Grunenfelder(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 θ_{n} for finite Abelian groups. In view of proposition 3.25 of (3) it is enough to consider finite Abelian p-groups.

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Deposited On: | 25 Aug 2011 09:58 |

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