Factorization into Symmetries and Transvections of Given Conjugacy Classes
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 400-409
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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.
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
@article{10_4153_CMB_1992_053_5,
author = {Kn\"uppel, Frieder},
title = {Factorization into {Symmetries} and {Transvections} of {Given} {Conjugacy} {Classes}},
journal = {Canadian mathematical bulletin},
pages = {400--409},
year = {1992},
volume = {35},
number = {3},
doi = {10.4153/CMB-1992-053-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-053-5/}
}
TY - JOUR AU - Knüppel, Frieder TI - Factorization into Symmetries and Transvections of Given Conjugacy Classes JO - Canadian mathematical bulletin PY - 1992 SP - 400 EP - 409 VL - 35 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-053-5/ DO - 10.4153/CMB-1992-053-5 ID - 10_4153_CMB_1992_053_5 ER -
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