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Finite groups embeddable in division rings


Author: T. Y. Lam
Journal: Proc. Amer. Math. Soc. 129 (2001), 3161-3166
MSC (2000): Primary 12E15, 16Kxx, 20B05; Secondary 20D20, 20B07, 16U60
DOI: https://doi.org/10.1090/S0002-9939-01-05961-5
Published electronically: April 17, 2001
MathSciNet review: 1844988
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Abstract:

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
Email: lam@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-01-05961-5
Received by editor(s): March 13, 2000
Published electronically: April 17, 2001
Communicated by: Lance W. Small
Article copyright: © Copyright 2001 copyright retained by the author

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