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Free subgroups in maximal subgroups of GL1(D)

Mahdavi Hezavehi, M ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. DOI: 10.1006/jabr.2001.8782
  3. Publisher: 2001
  4. Abstract:
  5. Let D be a division algebra of finite dimension over its center F. Given a noncommutative maximal subgroup M of D*:= GL1(D), it is proved that either M contains a noncyclic free subgroup or there exists a maximal subfield K of D which is Galois over F such that K* is normal in M and M/K*≅Gal(K/F). Using this result, it is shown in particular that if D is a noncrossed product division algebra, then M does not satisfy any group identity. © 2001 Academic Press
  6. Keywords:
  7. Division ring ; Free subgroup ; Maximal subgroup
  8. Source: Journal of Algebra ; Volume 241, Issue 2 , 2001 , Pages 720-730 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0021869301987824