Products of commutators of dilatations Original Research Article

We consider the group SLnF of all n × n matrices with determinant 1 over a field. Let res A denote rank (A - I) for any A in GLnF. A matrix A set membership, variant GLnF is called a dilatation if A is similar to a matrix In−1 circled plus a (a ≠ 1). We prove that if F > 4, then every matrix A in SLnF is the product of at most [res A/2] + 1 commutators of dilatations for n ≥ 2.