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

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• 作者：Mojtaba Ramezan-Nassab ; Dariush Kiani
• 关键词：12E15 ; 16K40 ; 16R20 ; 20E28
• 刊名：Journal of Algebra
• 出版年：1 February, 2014
• 年：2014
• 卷：399
• 期：Complete
• 页码：269-276
• 全文大小：207 K

文摘

Let D be an infinite division ring, n a natural number and N a subnormal subgroup of such that 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) (which asserts that each maximal subgroup of is abelian) and a result in Ramezan-Nassab and Kiani (2013) . In the second one we show that a maximal subgroup of cannot be polycyclic-by-finite.