on products of conjugacy classes in general linear groups

Let k be a field and n ≥ 3. let en(k) ≤ h ≤ gln(k) be an intermediate group and c anoncentral h-class. define m(c) as the minimal positive integer m such that ∃i1, . . . , im ∈ {±1} suchthat the product c^i1· · · c^im contains all nontrivial elementary transvections. in this article we obtaina sharp upper bound for m(c). moreover, we determine m(c) for any noncentral h-class c under theassumption that k is algebraically closed or n = 3 or n = ∞.