On a question of M. Newman on the number of commutators

R. K. Dennis; L. N. Vaserstein

doi:10.1016/0021-8693(88)90055-5

On a question of M. Newman on the number of commutators

R. K. Dennis, L. N. Vaserstein

Mathematics

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50 Scopus citations

Abstract

M. Newman asked whether there is an absolute constant c such that every matrix in SL_nR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ≥ 3. We give here a negative answer. However, if for the ring R every matrix in SL_mR is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SL_nR is the product of six commutators.

Original language	English (US)
Pages (from-to)	150-161
Number of pages	12
Journal	Journal of Algebra
Volume	118
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(88)90055-5
State	Published - Oct 1988

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/0021-8693(88)90055-5

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abstract = "M. Newman asked whether there is an absolute constant c such that every matrix in SLnR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ≥ 3. We give here a negative answer. However, if for the ring R every matrix in SLmR is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SLnR is the product of six commutators.",

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AB - M. Newman asked whether there is an absolute constant c such that every matrix in SLnR is the product of at most c commutators, where R ranges over euclidean commutative rings and n ≥ 3. We give here a negative answer. However, if for the ring R every matrix in SLmR is the product of a bounded number of commutators for some fixed m ≥ 3, then for all sufficiently large n, every matrix in SLnR is the product of six commutators.

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On a question of M. Newman on the number of commutators

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