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Modular augmentation ideals

Published online by Cambridge University Press:  24 October 2008

Robert Sandling
Robert Sandling
Affiliation:
The University, Manchester
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Extract

An ideal of an integral group ring is divisible by a given integer if all of its elements share this common factor; the ideals most often encountered are rarely divisible in this sense. Only in the case of finite p-groups are powers of the augmentation ideal of the integral group ring ever divisible. For every e, there is some n for which the nth power of the augmentation ideal is divisible by pe. The smallest such integer n arises in many contexts; this paper describes its properties and interpretations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 1 , January 1972 , pp. 25 - 32
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Bachmuth, S., Heilbronn, H. A. and Mochizuki, H. Y.Burnside metabelian groups. Proc. Roy. Soc. A 307 (1968), 235–250.Google Scholar
(2)Bachmuth, S. and Hughes, I.Centers of certain presentations of finite groups. Notices Amer. Math. Soc. 13 (1966), 576.Google Scholar
(3)Curtis, C. and Reiner, I.Representation theory of finite groups and associative algebras (Interscience, New York, 1962).Google Scholar
(4)Huppert, B.Endliche Oruppen I (Springer, Berlin, 1967).Google Scholar
(5)Jennings, S. A.The structure of the group ring of a p-group over a modular field. Trans. Amer. Math. Soc. 50 (1941), 175–185.Google Scholar
(6)Liebeck, H.Concerning nilpotent wreath products. Proc. Cambridge Philos. Soc. 58 (1962), 443–451.CrossRefGoogle Scholar
(7)Sandling, R. The modular group rings of p-groups. Thesis, Univ. of Chicago, 1969.Google Scholar
(8)Sandling, R. Dimension subgroups over arbitrary coefficient rings, to appear. J. Algebra.Google Scholar
(9)Sandling, R.Subgroups dual to dimension subgroups. Proc. Cambridge Philos. Soc. 71 (1972), 33–38.Google Scholar