On the compositum of all degree extensions of a number field
Itamar Gal, Robert Grizzard (2014)
Journal de Théorie des Nombres de Bordeaux
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We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of...