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Paper   IPM / M / 11156
School of Mathematics
  Title:   Maximal subgroups of GLn(D) with finite conjugacy classes
  Author(s):  D. Kiani (Joint with M. Ramezan-Nassab)
  Status:   To Appear
  Journal: Manuscripta Math.
  Supported by:  IPM
  Abstract:
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D* is an FC-group, then D is a field. Let M be a maximal subgroup of GLn(D), where n ≥ 1. In this paper we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of Mn(D). Moreover, if M is algebraic over Z(D), then [D:Z(D)] < ∞.

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