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The subnormal structure of general linear groups

Published online by Cambridge University Press:  24 October 2008

L. N. Vaserstein
L. N. Vaserstein
Affiliation:
Institute for Advanced Study, Princeton and Pennsylvania State University
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Let A be an associative ring with 1. For any natural number n, let GLnA denote the group of invertible n by n matrices over A, and let EnA be the subgroup generated by all elementary matrices ai, j, where aεA and 1 ≤ i ≡ j ≤ n. For any (two-sided) ideal B of A, let GLnB be the kernel of the canonical homomorphism GLnA→GLn(A/B) and Gn(A, B) the inverse image of the centre of GLn(A/B) (when n > 1, the centre consists of scalar matrices over the centre of the ring A/B). Let EnB denote the subgroup of GLnB generated by its elementary matrices, and let En(A, B) be the normal subgroup of EnA generated by EnB (when n > 2, the group GLn(A, B) is generated by matrices of the form ai, jbi, j(−a)i, j with aA, b in B, i ≡ j, see [7]). In particuler,

is the centre of GLnA

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 425 - 431
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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