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

Published electronically:
April 17, 2001

MathSciNet review:
1844988

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
http://dx.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