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An embedding theorem for fields

Published online by Cambridge University Press:  17 April 2009

J.W.S. Cassels
J.W.S. Cassels
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK.
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Abstract

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It is shown that every finitely generated field K of characteristic 0 may be embedded in infinitely many p-adic fields in such a way that the images of any given finite set C of non-zero elements of K are p-adic units. The result is suggested by Lech's proof of his generalization of Mahler's theorem on recurrent sequences. It also provides a simple proof of Selberg's theorem about torsion-free normal subgroups of matrix groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 2 , April 1976 , pp. 193 - 198
Copyright
Copyright © Australian Mathematical Society 1976

References

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