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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite groups embeddable in division rings
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by T. Y. Lam PDF
Proc. Amer. Math. Soc. 129 (2001), 3161-3166


In a tour de force in 1955, S. A. Amitsur classified all finite groups that are embeddable in division rings. In particular, he disproved a conjecture of Herstein which stated that odd-order emdeddable groups were cyclic. The smallest counterexample turned out to be a group of order 63. In this note, we prove a non-embedding result for a class of metacyclic groups, and present an alternative approach to a part of Amitsur’s results, with an eye to “de-mystifying" the order 63 counterexample.
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Additional Information
  • T. Y. Lam
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 109495
  • Email:
  • Received by editor(s): March 13, 2000
  • Published electronically: April 17, 2001
  • Communicated by: Lance W. Small
  • © Copyright 2001 copyright retained by the author
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3161-3166
  • MSC (2000): Primary 12E15, 16Kxx, 20B05; Secondary 20D20, 20B07, 16U60
  • DOI:
  • MathSciNet review: 1844988