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

JOURNAL OF ALGEBRA

卷:399

Article

Ramezan-Nassab, Mojtaba¹  Kiani, Dariush¹ 

[1] Amirkabir Univ Technol, Tehran Polytech, Dept Math & Comp Sci, Tehran, Iran

关键词: Division ring;    Maximal subgroup;    Nilpotent group;    Polycyclic-by-finite group;   

DOI  :  10.1016/j.jalgebra.2013.09.042

来源: Elsevier

【 摘 要 】

Let D be an infinite division ring, n a natural number and N a subnormal subgroup of GL(n)(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 GL(n)(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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free