(Locally soluble)-by-(locally finite) maximal subgroups of GLn(D)

JOURNAL OF ALGEBRA

卷:376

Article

Ramezan-Nassab, M.^1,2  Kiani, D.^1,2 

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

[2] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

关键词: Division ring;    Skew linear group;    Maximal subgroup;    Locally soluble;    Locally finite;   

DOI  :  10.1016/j.jalgebra.2012.11.024

来源: Elsevier

【 摘 要 】

Let D be a non-commutative division ring and M a maximal subgroup of GLn(D) (n >= 2). This paper continues the ongoing effort to show that the structure of maximal subgroups of GL(n)(D) is similar, in some sense, to the structure of GL(n)(D). It is known that every locally soluble normal subgroup of GL(n)(D) is abelian. Here, among other results, we prove that if either (i) D is finite-dimensional over its center, or (ii) the center of D contains at least five elements and M is soluble-by-finite, or (iii) char D = 0 and M is (locally soluble)-by-finite, then every locally soluble normal subgroup of M is abelian. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free