The extended covering number of \(\text{SL}_n\) is \(n+1\).

DOI10.1016/j.laa.2006.03.011zbMath1104.20047OpenAlexW2007952237MaRDI QIDQ855554

Frieder Knüppel, Klaus Nielsen

Publication date: 7 December 2006

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2006.03.011

zbMATH Keywords

conjugacy classesspecial linear groupsextended covering numberslength theorems

Mathematics Subject Classification ID

Factorization of matrices (15A23) Conjugacy classes for groups (20E45) Linear algebraic groups over arbitrary fields (20G15) Generators, relations, and presentations of groups (20F05) Classical groups (algebro-geometric aspects) (14L35)

Related Items (4)

On products of conjugacy classes in general linear groups ⋮ Elementary covering numbers in odd-dimensional unitary groups ⋮ Covering GL(V) and products of blockcyclic matrices ⋮ Covering singular linear semi-groups

Cites Work

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• Antiinvariant subspaces of maximum dimension
• Cycles comme produit de deux permutations de classes données
• \(GL^{\pm{}}_ n(R)\) is 5-reflectional
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• \(k\)-fold anti-invariant subspaces of a linear mapping.
• Products of conjugacy classes of two by two matrices
• Products of similar matrices
• The covering number of the group \(\text{PSL}_ n(F)\)
• Products of conjugacy classes in groups
• Regular elements of semisimple algebraic groups
• Similarity of matrices under SL(n,K)
• Similarity overSL(n, F)
• Distribution of irreducible polynomials of small degrees over finite fields
• Products of Conjugacy Classes in the Special Linear Groups
• On sums and products of Matrix similarity classes I
• A matrix-decomposition theorem for \(\text{GL}_n(K)\)

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