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 a ≤ b 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.
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Dedicated to Professors Antanas Laurinčikas and Eugenijus Manstavičius on the occasion of their 70th birthdays
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* This research was funded by a grant (No. S-MIP-17-66/LSS-110000-1274) from the Research Council of Lithuania.
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Drungilas, P., Maciulevičius, L. A degree problem for the compositum of two number fields*. Lith Math J 59, 39–47 (2019). https://doi.org/10.1007/s10986-019-09428-x
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DOI: https://doi.org/10.1007/s10986-019-09428-x