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Sibirskii Matematicheskii Zhurnal, 2006, Volume 47, Number 5, Pages 1160–1166
(Mi smj922)
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This article is cited in 7 scientific papers (total in 7 papers)
Infinite dimensional general linear groups have finite width
V. A. Tolstykh Kemerovo State University
Abstract:
A group is said to have finite width whenever it has finite width with respect to each inverse-closed generating set. Bergman showed [1] that infinite symmetric groups have finite width and asked whether the automorphism groups of several classical structures have finite width, mentioning in particular infinite dimensional general linear groups over fields. In this article we prove that infinite dimensional general linear groups over arbitrary division rings have finite width. We consider the problem of finite width for other infinite dimensional classical groups.
Keywords:
general linear group, infinite-dimensional vector space, generating set, width.
Received: 21.11.2005
Citation:
V. A. Tolstykh, “Infinite dimensional general linear groups have finite width”, Sibirsk. Mat. Zh., 47:5 (2006), 1160–1166; Siberian Math. J., 47:5 (2006), 950–954
Linking options:
https://www.mathnet.ru/eng/smj922 https://www.mathnet.ru/eng/smj/v47/i5/p1160
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