The structure of linear PF-Engel groups in characteristic zero

Suppose G is linear group. If G has characteristic zero, we prove that G is (polycyclic-by-finite)-Engel if and only if G has a normal series < 1 > = T-0 <= T-1 <= center dot center dot center dot <= T-s = T <= G with s and the index (G:T) finite and each T-i/Ti-1 either polycyclic-by-finite, or G-hypercentral with [T-i, T] <= Ti-1, or G-hypercentral, abelian and Chernikov. This is much more complex than the positive characteristic case where G is (polycyclic-by-finite)-Engel if and only if G is (polycyclic-by-finite)-by-hypercentral.