Finite groups embeddable in division rings

Lam, T.

doi:10.1090/S0002-9939-01-05961-5

Finite groups embeddable in division rings
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by T. Y. Lam PDF

Proc. Amer. Math. Soc. 129 (2001), 3161-3166

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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