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The normal subgroup structure of the infinite general linear group

Published online by Cambridge University Press:  20 January 2009

David G. Arrell
David G. Arrell
Affiliation:
School of Mathematics and Computing, Leeds Polytechnic, Leeds LS1 3HE
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The classification of the normal subgroups of the infinite general linear group GL(Ω, R) has received much attention and has been studied in, for example, (6), (4) and (2). The main theorem of (6) gives a complete classification of the normal subgroups of GL(Ω, R) when R is a division ring, while the results of (2) require that R satisfies certain finiteness conditions. The object of this paper is to produce a classification, along the lines of that given by Wilson in (7) or by Bass in (3) in the finite dimensional case, that does not require any finiteness assumptions. However, when R is Noetherian, the classification given here reduces to that given in (2).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 3 , October 1981 , pp. 197 - 202
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Arrell, D. G., Infinite dimensional linear and symplectic groups (Ph.D. thesis, University of St Andrews, 1979).Google Scholar
(2)Arrell, D. G. and Robertson, E. F., Infinite dimensional linear groups, Proc. Roy. Soc. Edinburgh 78A (1978), 237–240.CrossRefGoogle Scholar
(3)Bass, H., Algebraic K-theory (Benjamin, New York-Amsterdam, 1968).Google Scholar
(4)Maxwell, G., Infinite general linear groups over rings, Trans. Amer. Math. Soc. 151 (1970), 371–375.CrossRefGoogle Scholar
(5)Robertson, E. F., A remark on the derived group of GL(R), Bull. London Math. Soc. 1 (1969), 160–162.CrossRefGoogle Scholar
(6)Rosenberg, A., The structure of the infinite general linear group, Ann. of Math. (2) 68 (1958), 278–294.CrossRefGoogle Scholar
(7)Wilson, J. S., The normal and subnormal subgroup structure of the general linear group, Proc. Cambridge Philos. Soc. 71 (1972), 163–177.CrossRefGoogle Scholar