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Crossed product conditions for division algebras of prime power degree

Kiani, D ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jalgebra.2004.04.022
  3. Publisher: 2005
  4. Abstract:
  5. Let D be an F-central division algebra of degree pr, 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. © 2004 Elsevier Inc. All rights reserved
  6. Keywords:
  8. Source: Journal of Algebra ; Volume 283, Issue 1 , 2005 , Pages 222-231 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0021869304004314