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Tits alternative for maximal subgroups of skew linear groups

Kiani, D ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1080/00927870903400063
  3. Publisher: 2010
  4. Abstract:
  5. Let D be a noncommutative finite dimensional F-central division algebra, and let N be a normal subgroup of GLn(D) with n≥1. Given a maximal subgroup M of N, it is proved that either M contains a noncyclic free subgroup, or there exists an abelian subgroup A and a finite family {Ki}1 r of fields properly containing F with Ki* ∩ N ⊃ M for all 1 ≤ i ≤ r such that M/A is finite if Char F = 0 and M/A is locally finite if Char F = p > 0, where A ⊆ K1* ×...× Kr*
  6. Keywords:
  7. Maximal subgroup ; Skew linear group
  8. Source: Communications in Algebra ; Volume 38, Issue 6 , Jun , 2010 , Pages 2354-2363 ; 00927872 (ISSN)
  9. URL: http://www.tandfonline.com/doi/abs/10.1080/00927870903400063?journalCode=lagb20