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Abundant central extensions of non-trivial genera

Published online by Cambridge University Press:  22 January 2016

K. Miyake  and
N. Ormerod
K. Miyake
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Nagoya 464, Japan
N. Ormerod
Affiliation:
School of Mathematics, The University of New South Wales, PO Box 1, Kensington N.S.W. 2033, Australia
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Let k be either a local or a global field, and K be a finite Galois extension of k with g = Gal (K/k). Let L be a Galois extension of K which is also Galois over k. Such an extension is called central if Gal(L/iT) lies inside the centre of Gal(L/K). Clearly L is abelian over K. Next set L* = L∩K · kab where kab is the maximal abelian extension of k in its algebraic closure. This is the genus field of L over K/k.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 95 , September 1984 , pp. 51 - 62
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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