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The Quarterly Journal of Mathematics Advance Access originally published online on July 18, 2006
The Quarterly Journal of Mathematics 2007 58(1):127-135; doi:10.1093/qmath/hal012
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

NORMALIZERS OF NILPOTENT SUBGROUPS OF DIVISION RINGS

B. A. F. Wehrfritz{dagger}

School of Mathematical Sciences, Queen Mary College, University of London, Mile End Road, London E1 4NS

{dagger} E-mail: b.a.f.wehrfritz{at}qmul.ac.uk

Received 27 March 2006; revised 6 June 2006
  Abstract

Let D be an arbitrary division ring and G a nilpotent subgroup of the multiplicative group D* of D of class at most 2 such that D is generated as a division ring by G and the centralizer in D of G. The normalizer of G in D* is computed precisely, which extends a theorem of M. Shirvani from finite-dimensional division algebras to arbitrary division rings.


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