Geodesic
Factorization into Symmetries and Transvections of Given Conjugacy Classes
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 400-409

Voir la notice de l'article provenant de la source Cambridge University Press

The u-invariant u(K) of a field K is the smallest number such that every k-dimensional regular quadratic form over K is universal. Let O(V,f) be the orthogonal group of a finite-dimensional regular metric vector space over a field K of characteristic distinct from 2. Let π ∊ 0(V), B(π) := V(π - 1), dim[B(π) ∩ kernel(π - 1)] > u(K). Given λ1,..., λm ∊ K* where m := dim B(π) - u(K) + 1. Then π = σ1······σk where k := dim B(π) and σi is a symmetry with negative space Kai and f(ai, ai) = λi for i ∊ { 1 , . . . , m}. We prove similar theorems also for symplectic groups where transvections are taken as generators.
DOI : 10.4153/CMB-1992-053-5
Mots-clés : 51N30, 11E57, 15A23, 14L35 
Knüppel, Frieder. Factorization into Symmetries and Transvections of Given Conjugacy Classes. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 400-409. doi: 10.4153/CMB-1992-053-5
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