Generators for classical groups of modules over local rings

DOI10.1007/BF01222140zbMath0716.20027MaRDI QIDQ752855

Erich W. Ellers, Huberta Lausch

Publication date: 1990

Published in: Journal of Geometry (Search for Journal in Brave)

zbMATH Keywords

free modulecommutative local ringfactorizations of isometriesminimal number of factorsset of generatorssimple mappings

Mathematics Subject Classification ID

Factorization of matrices (15A23) Generators, relations, and presentations of groups (20F05) Matrices over special rings (quaternions, finite fields, etc.) (15B33) Other geometric groups, including crystallographic groups (20H15) Linear transformations, semilinear transformations (15A04) Reflection groups, reflection geometries (51F15) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (6)

Pappian affine Klingenberg planes ⋮ A comparison of length definitions for maps of modules over local rings ⋮ Linear groups over general rings. I: Generalities. ⋮ Width of groups of type \(\mathrm E_6\) with respect to root elements. II. ⋮ The width of the group \(\mathrm{GL}(6,K)\) with respect to a set of quasiroot elements. ⋮ Width of groups of type $\mathrm E_{6}$ with respect to root elements. I

Cites Work

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• Factorization of transformations over a local ring
• Products of quasireflections and transvections over local rings
• Generators of \(Sp_ n(\)V) over a quasi semilocal semihereditary ring
• Decomposition of orthogonal, symplectic, and unitary isometries into simple isometries
• Generators of an orthogonal group over a local valuation domain
• Unverkürzbare Produkte und Relationen in unitären Gruppen
• Über die Erzeugenden der engeren unitären Gruppen
• On the Decomposition of Orthogonalities into Symmetries

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