The elements of the special linear group \(\text{SL}_nF\) as products of commutators of transvections (Q2767427)

Let \(F\) be a field with more than three elements and let \(\text{SL}_nF\) be the special linear group. For \(A\in\text{SL}_nF\) define \(\text{res }A=\text{rank }(A-I)\). As generators for \(\text{SL}_nF\) the authors choose the commutators of elements \(T\in\text{SL}_nF\) with \(\text{res }T=1\). They show that every element in \(\text{SL}_nF\) is a product of \([(\text{res }A)/2]+2\) or fewer of these generators.