Let R be a commutative local ring with the unique maximal ideal A. Let V be a ลฝ . free module of rank n over R. And let Sp V be the symplectic group on V with n an alternating bilinear form f : V = V ยช R. We study the generation of a subgroup author's conjecture in ''Generators and Relations in Gro
โฆ LIBER โฆ
Generation of special linear groups by transvections
โ Scribed by Stephen P. Humphries
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 895 KB
- Volume
- 99
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
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If \(R\) is a division ring and \(n \geq 2\), then we give an elegant, basis free, presentation for the general linear group \(G L_{n}(R)\) in terms of transvections and dilations. In case \(R\) is a field, we give a similar presentation for \(S L_{n}(R)\), but now purely in terms of transvections.
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