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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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- Copyright © Canadian Mathematical Society 2002
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