Crossed product conditions for division algebras of prime power degree

被引:4
作者
Kiani, D [1 ]
Mahdavi-Hezavehi, M [1 ]
机构
[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran
关键词
D O I
10.1016/j.jalgebra.2004.04.022
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let D be an F-central division algebra of degree P-r, p a prime. A set of criteria is given for D to be a crossed product in terms of irreducible soluble or abelian-by-finite subgroups of the multiplicative group D* of D. Using the Amitsur's classification of finite subgroups of D* and the Tits alternative, it is shown that D is a crossed product if and only if D* contains an irreducible soluble subgroup. Further criteria are also presented in terms of irreducible abelian-by-finite subgroups and irreducible subgroups satisfying a group identity. Using the above results, it is shown that if D* contains an irreducible finite subgroup, then D is a crossed product. (C) 2004 Elsevier Inc. All rights reserved.
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页码:222 / 231
页数:10
相关论文
共 10 条
  • [1] EBRAHIMIAN R, IN PRESS COMM ALGEBR
  • [2] EBRAHIMIAN R, IN PRESS ISRAEL J MA
  • [3] LAM TY, 1991, GRAD TEXTS MATH, V131
  • [4] Cyclicity conditions for division algebras of prime degree
    Mahdavi-Hezavehi, M
    Tignol, JP
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (12) : 3673 - 3676
  • [5] Free subgroups in maximal subgroups of GL1(D)
    Mahdavi-Hezavehi, M
    [J]. JOURNAL OF ALGEBRA, 2001, 241 (02) : 720 - 730
  • [6] Rowen LH., 1980, POLYNOMIAL IDENTITIE
  • [7] Scott W. R., 1987, GROUP THEORY
  • [8] Shirvani M., 1986, London Math. Soc. Lecture Note Ser., V118
  • [9] SUPRUNENKO DA, 1965, AM MATH SOC TRANSL, V2, P153
  • [10] ZALESSKII AE, 1993, ALGEBRA 2, V4