Existence of Nonabelian Free Subgroups in the Maximal Subgroups of GLn（D）

作     者：H.R. Dorbidi R. Fallah-Moghaddam M. Mahdavi-Hezavehi 

作者机构：Department of Mathematical Sciences Sharif University of 3bchnology P.O. Box 11155-3415 Tehran Iran 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2014年第21卷第3期

页      面：483-496页

核心收录：

学科分类：0832[工学-食品科学与工程（可授工学、农学学位）] 07[理学] 08[工学] 070104[理学-应用数学] 083201[工学-食品科学] 0701[理学-数学] 

基　　金：Research Council of Sharif University of Technology 

主　　题：free subgroup maximal subgroup central simple algebralotion 

摘      要：Given a non-commutative finite dimensional F-central division algebra D, we study conditions under which every non-abelian maximal subgroup M of CLn （D） contains a non-cyclic free subgroup. In general, it is shown that either M contains a non-cyclic free subgroup or there exists a unique maximal subfield K of Mn（D） such that NCLn（D）（K＊） = M, K＊ △ M, K/F is Galois with Gal（K/F） ≌ M/K＊, and F[M] = in（D）. In particular, when F is global or local, it is proved that if （[D ： F], Char（F）） = 1, then every non- abelian maximal subgroup of GL1 （D） contains a non-cyclic free subgroup. Furthermore, it is also shown that GLn（F） contains no solvable maximal subgroups provided that F is local or global and n ≥ 5.