The extended covering number of SLn is n + 1

For a special linear group SLn (K) (K a field) we want to find the minimal integer k (extended covering number) such that 1 ∈ C1 ⋯ Ck for arbitrary non-central conjugacy classes Ci of SLn (K). Using methods from Chevalley groups, length-theorems on products of simple mappings and theorems on products of cyclic mappings we find that k = n + 1, provided n and the field are not too small.