Abstract
M. Newman asked whether there is an absolute constant c such that every matrix in SL n R 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 m R is the product of a bounded number of commutators for some fixed m ⩾ 3, then for all sufficiently large n, every matrix in SL n R is the product of six commutators.
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