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On central extensions of a Galois extension of algebraic number fields
Published online by Cambridge University Press: 22 January 2016
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Let k be an algebraic number field of finite degree, and K a finite Galois extension of k. A central extension L of K/k is an algebraic number field which contains K and is normal over k, and whose Galois group over K is contained in the center of the Galois group Gal(L/k). We denote the maximal abelian extensions of k and K in the algebraic closure of k by kab and Kab respectively, and the maximal central extension of K/k by MCK/k. Then we have Kab⊃MCK/k⊃kab·K.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1984
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