The Kneser-Tits conjecture for groups with Tits-index E_8,2⁶⁶ over an arbitrary field

2010/08/11 by R. Parimala, Jean-Pierre Tignol, Parimala, R. +3
Mathematics · #11E04 #20G15 #20G41 #51E12 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1008.1868

openalex publication_date 2010/08/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove: (1) The group of multipliers of similitudes of a 12-dimensional anisotropic quadratic form over a field K with trivial discriminant and split Clifford invariant is generated by norms from quadratic extensions E/K such that q_E is hyperbolic. (2) If G is the group of K-rational points of an absolutely simple algebraic group whose Tits index is E_8,2⁶⁶, then G is generated by its root groups, as predicted by the Kneser-Tits conjecture.

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