Overgroups in GL(nr,F) of certain subgroups of SL(n,K). I (Q1122660)

Let K and F be division rings with \(K\supseteq F\) and left \(\dim_ FK=r\) finite. The author determines all overgroups of SL(n,K) in GL(nr,F). If K is commutative and n is even he also finds all overgroups of Sp(n,K) in GL(nr,F). The author promises to determine all overgroups of SU(n,K,f) and \(\Omega\) (n,K,Q) in GL(nr,F) in a later paper.