Commutator width in Chevalley groups


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.

DOI Code: 10.1285/i15900932v33n1p139

Keywords: Chevalley groups; elementary subgroups; elementary generators; commutator width; relative groups; bounded generation; standard commutator formulas; unitriangular factorisations

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