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On Cyclic Fields of Odd Prime Degree p with Infinite Hilbert p-Class Field Towers
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $k$ be a cyclic extension of odd prime degree
$p$ of the field of rational numbers. If
$t$ denotes the number of primes that ramify in
$k$, it is known that the Hilbert
$p$-class field tower of
$k$ is infinite if
$t\,>\,3\,+\,2\sqrt{p}$. For each
$t\,>\,2\,+\,\sqrt{p}$, this paper shows that a positive proportion of such fields
$k$ have infinite Hilbert
$p$-class field towers.
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- Research Article
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- Copyright © Canadian Mathematical Society 2002
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