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Locally finite conditions on maximal subgroups of GL n(D)

Fallah Moghaddam, R ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. Publisher: 2012
  3. Abstract:
  4. Given a division ring D with center F, the structure of maximal subgroups M of GL n(D) is investigated. Suppose D ≠ F or n > 1. It is shown that if M/(M ∩ F*) is locally finite, then char F = p > 0 and either n = 1, [D:F] = p 2 and M ∪ {0} is a maximal subfield of D, or D = F, n = p, and M ∪ {0} is a maximal subfield of M p(F), or D = F and F is locally finite. It is also proved that the same conclusion holds if M/(M ∩ F*) is torsion and D is of finite dimension over F. Furthermore, it is shown that if the r-th derived group M (r) of M is locally finite, then either M (r) is abelian or F is algebraic over its prime subfield
  5. Keywords:
  6. Division ring ; Locally finite ; Maximal subgroup
  7. Source: Algebra Colloquium ; Volume 19, Issue 1 , 2012 , Pages 73-86 ; 10053867 (ISSN)
  8. URL: http://www.worldscientific.com/doi/abs/10.1142/S1005386712000053