Commutator width in Chevalley groups

Abstract

The present paper is the [slightly expanded] text of our talk at the Conference "Advances in Group Theory and Applications" at Porto Cesareo in June 2011. Our main results assert that [elementary] Chevalley groups very rarely have finite commutator width. The reason is that they have very few commutators, in fact, commutators have finite width in elementary generators. We discuss also the background, bounded elementary generation, methods of proof, relative analogues of these results, some positive results, and possible generalisations.

References in corpus (5)

• Structure of Chevalley groups over rings via universal localization
• The yoga of commutators
• Gauss decomposition for Chevalley groups, revisited
• Unitriangular factorisations of Chevalley groups
• Multiple Commutator Formulas for Unitary Groups

Cited by in corpus (8)

• Structure of Chevalley groups over rings via universal localization
• Word equations in simple groups and polynomial equations in simple algebras
• Generation of relative commutator subgroups in Chevalley groups. II
• Commutators of relative and unrelative elementary subgroups in Chevalley groups
• Commutators of relative and unrelative elementary unitary groups
• Multiple Commutator Formulas for Unitary Groups
• Bounded reduction of orthogonal matrices over polynomial rings
• The reverse decomposition of unipotents for bivectors