Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T13:46:30.060Z Has data issue: false hasContentIssue false
  • English
  • Français

The subnormal subgroup structure of the infinite symplectic 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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a ring with identity and let Ω be a totally ordered set. Let Ω′ be a totally ordered set which is disjoint from and equipotent to Ω′ with ′:Ω→Ω′ an order preserving bijection. Define Ω1=Ω∪Ω′ and let Ω1, be totally ordered by inheriting the order from Ω and Ω′ and with ω<λ for all ω∈Ω and λ′∈Ω′. Let M be the free R-module R(Ω1).(We define the alternate bilinear form (*, *) on M by

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 3 , October 1982 , pp. 209 - 216
Copyright
Copyright © Edinburgh Mathematical Society 1982

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., The normal subgroup structure of the infinite general linear group; Proc. Edinburgh Math. Soc. 24 (1981), 197–202.CrossRefGoogle Scholar
(3) Bass, H., Algebraic K-theory (Benjamin, New York-Amsterdam, 1968).Google Scholar
(4) Dieudonne., J., On the structure of the unitary groups, Trans. Amer. Math. Soc. 72 (1952), 367–385.CrossRefGoogle Scholar
(5) Dieudonne., J., On the structure of the unitary groups, II, Amer. J. Math. 75 (1953), 665–678.CrossRefGoogle Scholar
(6) Maxwell., G., Infinite symplectic groups over rings, Comment. Math. Helv. 47 (1972), 254–259.CrossRefGoogle Scholar
(7) Robertson., E. F.; Some properties of SpΩ(R), J. London Math. Soc. (2) 4 (1971), 65–78.Google Scholar
(8) Spiegel., E., On the structure of the infinite dimensional unitary group, Math. Annalen 172 (1967), 197–202.CrossRefGoogle Scholar
(9) Wilson., J. S., The normal and subnormal structure of the general linear group, Proc. Cambridge Philos. Soc. 71 (1972), 163–177.CrossRefGoogle Scholar