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Nilpotent subgroups of finite‐dimensional division algebras

Nilpotent subgroups of finite‐dimensional division algebras Let D be a division ring of finite degree d and suppose that G is a nilpotent subgroup of the multiplicative group D* of D. We determine the structure of G in terms of d. We produce examples showing that our results are close to the best possible. Our descriptions focus mainly on the centre factor group and the derived subgroup of G. The results are uniform except for some anomalies caused by the prime 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Nilpotent subgroups of finite‐dimensional division algebras

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References (3)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdm001
Publisher site
See Article on Publisher Site

Abstract

Let D be a division ring of finite degree d and suppose that G is a nilpotent subgroup of the multiplicative group D* of D. We determine the structure of G in terms of d. We produce examples showing that our results are close to the best possible. Our descriptions focus mainly on the centre factor group and the derived subgroup of G. The results are uniform except for some anomalies caused by the prime 2.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Jun 1, 2007

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