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|Paper IPM / M / 11156||
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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