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Finite groups embeddable in division rings
Author(s):
T.
Y.
Lam
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3161-3166.
MSC (2000):
Primary 12E15, 16Kxx, 20B05;
Secondary 20D20, 20B07, 16U60
Posted:
April 17, 2001
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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.
References:
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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:
10.1090/S0002-9939-01-05961-5
PII:
S 0002-9939(01)05961-5
Received by editor(s):
March 13, 2000
Posted:
April 17, 2001
Communicated by:
Lance W. Small
Copyright of article:
Copyright
2001,
copyright retained by the author
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