  Let D be an infinite division ring, n a natural number and N a subnormal
subgroup of GLn(D) such that n = 1 or the center of D contains at least five
elements. This paper contains two main results. In the first one we prove that
each nilpotent maximal subgroup of N is abelian; this generalizes the result in
[R. Ebrahimian, J. Algebra 280 (2004) 244 - 248] (which asserts that each max-
imal subgroup of GLn(D) is abelian) and a result in [M. Ramezan-Nassab, D.
Kiani, J. Algebra 376 (2013) 1 - 9]. In the second one we show that a maximal
subgroup of GLn(D) cannot be polycyclic-by-finite.
