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Paper   IPM / M / 8563
School of Mathematics
  Title:   Polynomial identities and maximal subgroups of skew linear groups
  Author(s):  D. Kiani
  Status:   Published
  Journal: Manuscripta Math.
  Vol.:  124
  Year:  2007
  Pages:   269-274
  Supported by:  IPM
Suppose that D is a division ring with center F and N is a non-central normal subgroup of GLn(D). In this paper we generalize some known results about maximal subgroups of GLn(D) to maximal subgroups of N. More precisely we prove that if M is a maximal subgroup of N such that F[M] satisfies a polynomial identity and CMn(D)(M)\F contains an algebraic element over F or CMn(D)(M) = F and either n ≥ 2 or n = 1 and M is not abelian, then [D: F] < ∞.

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