Nilpotent and polycyclic-by-finite maximal subgroups of skew linear groups

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 Ebrahimian (2004) [3] (which asserts that each maximal subgroup of GLn(D) is abelian) and a result in Ramezan-Nassab and Kiani (2013) [12]. In the second one we show that a maximal subgroup of GLn(D) cannot be polycyclic-by-finite.