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Cyclicity conditions for division algebras of prime degree


Authors: M. Mahdavi-Hezavehi and J.-P. Tignol
Journal: Proc. Amer. Math. Soc. 131 (2003), 3673-3676
MSC (2000): Primary 16K20
DOI: https://doi.org/10.1090/S0002-9939-03-06959-4
Published electronically: February 26, 2003
MathSciNet review: 1998187
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $D$ be a division algebra of prime degree $p$. A set of criteria is given for cyclicity of $D$in terms of subgroups of the multiplicative group $D^*$ of $D$. It is essentially shown that $D$ is cyclic if and only if $D^*$contains a nonabelian metabelian subgroup.


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Additional Information

M. Mahdavi-Hezavehi
Affiliation: Department of Mathematical Sciences, Sharif University of Technology, P. O. Box 11365–9415, Tehran, Iran
Email: mahdavih@sharif.edu

J.-P. Tignol
Affiliation: Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
Email: tignol@math.ucl.ac.be

DOI: https://doi.org/10.1090/S0002-9939-03-06959-4
Received by editor(s): June 19, 2002
Received by editor(s) in revised form: July 15, 2002
Published electronically: February 26, 2003
Additional Notes: The first author thanks the Research Council of Sharif University of Technology for support. He also thanks Professor J.-P. Tignol for his hospitality during his stay at the Université Catholique de Louvain in May 2002.
The second author was partially supported by the National Fund for Scientific Research (Belgium).
Communicated by: Martin Lorenz
Article copyright: © Copyright 2003 American Mathematical Society