Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T09:54:18.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Dimension subgroups modulo n

Published online by Cambridge University Press:  24 October 2008

Siegfried Moran
Siegfried Moran
Affiliation:
University of Kent at Canterbury
Get access Rights & Permissions [Opens in a new window]

Extract

Let G be an arbitrary group and Zn(G) denote the group algebra of G over the integers modulo n. If δi(G) denotes ith power of the augmentation ideal δ(G) of Zn(G), then

is easily seen to be a normal subgroup of G. It is denoted by Di, n(G) and is called ith dimension subgroup of G modulo n. It can be shown that these dimension subgroups are determined by the dimension subgroups modulo a power of a prime p. Hence we shall restrict our attention to these dimension subgroups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 579 - 582
Copyright
Copyright © Cambridge Philosophical Society 1970

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)Jacobson, N.Lie algebras (In.terscience, New York, 1962).Google Scholar
(2)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
(3)Lazard, M.Sur les groupes nilpotents et les anneaux de Lie. Ann. Sci. École Norm. Sup. (3) 71 (1954), 101–190.CrossRefGoogle Scholar
(4)Zassenhaus, H.Ein Verfahren jeder endlichen p-Gruppe einem Lie-Ring mit der Charakteristik p zuzuordnen. Abh. Math. Sem. Univ. Hamburg 13 (1940), 200–207.CrossRefGoogle Scholar