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Paper IPM / M / 11156  


Abstract:  
Let D be an infinite division ring. A famous result due to
Herstein says that every noncentral element of D has infinitely
many conjugates and so, if D^{*} is an FCgroup, then D is a
field. Let M be a maximal subgroup of GL_{n}(D), where n ≥ 1. In this paper we prove that if M is an FCgroup, then it
is the multiplicative group of some maximal subfield of M_{n}(D).
Moreover, if M is algebraic over Z(D), then
[D:Z(D)] < ∞.
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