Elementary subgroup of an isotropic reductive group is perfect

2010/01/07 by Alexander Luzgarev, Anastasia Stavrova, Luzgarev, Alexander +1 · 1 citation
Mathematics · #20G07 #20G15 #20G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:20G07 #msc:20G15 #msc:20G35

paper · pdf · doi:10.48550/arxiv.1001.1105

10 pages

arxiv created 2010/01/07 · arxiv updated 2010/01/14

Abstract

Let G be an isotropic reductive algebraic group over a commutative ring R. Assume that the elementary subgroup E(R) of group of points G(R) is correctly defined. Then E(R) is perfect, except for the well-known cases of a split reductive group of type C₂ or G₂.

Cited by

• Abstract isomorphisms of isotropic root graded groups over rings

Related

• Locally isotropic elementary groups
• Centralizer of the elementary subgroup of an isotropic reductive group
• The Diophantine problem in isotropic reductive groups
• Normal structure of isotropic reductive groups over rings
• Isotropic reductive groups over discrete Hodge algebras