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Lithuanian Mathematical Journal

, Volume 59, Issue 1, pp 39–47 | Cite as

A degree problem for the compositum of two number fields*

  • Paulius DrungilasEmail author
  • Lukas Maciulevičius
Article
  • 27 Downloads

Abstract

The triplet (a, b, c) of positive integers is said to be compositum-feasible if there exist number fields K and L of degrees a and b, respectively, such that the degree of their compositum KL equals c. We determine all compositum-feasible triplets (a, b, c) satisfying ab and b ∈ {8, 9}. This extends the classification of compositum-feasible triplets started by Drungilas, Dubickas, and Smyth [5]. Moreover, we obtain several results related to triplets of the form (a, a, c). In particular, we prove that the triplet (n, n, n(n − 2)) is not compositum-feasible, provided that n ≥ 5 is an odd integer.

Keywords

algebraic number sum-feasible product-feasible compositum-feasible 

MSC

11R04 11R32 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of MathematicsVilnius UniversityVilniusLithuania

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