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The ideal lattices of the complex group rings of finitary special and general linear groups over finite fields

Published online by Cambridge University Press:  24 October 2008

B. Hartley  and
A. E. Zalesskii
B. Hartley
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL
A. E. Zalesskii
Affiliation:
Institute of Mathematics, Academy of Sciences of Belarus, 220072 Minsk, Belarus
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Extract

Let q be a prime power, which will be fixed throughout the paper, let k be a field, and let be the field with q elements. Let Gn(k) be the general linear group GL(n, k), and Sn(k) the special linear group SL(n, k). The corresponding groups over will be denoted simply by Gn and Sn. We may embed Gn(k) in Gn+1(k) via the map

Forming the direct limit of the resulting system, we obtain the stable general linear groupG∞(k) over k.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 1 , July 1994 , pp. 7 - 25
Copyright
Copyright © Cambridge Philosophical Society 1994

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