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<p>A triplet of positive integers (<i>a, b, c</i>) is said to be compositum-feasible if there exist number fields <i>K</i> and <i>L</i> of degrees <i>a</i> and <i>b</i>, respectively, such that the degree of their compositum <i>KL</i> equals <i>c</i>. In this paper, by applying the recently completed classification of almost simple groups of prime power degree, we discover previously unknown compositum-feasible triplets of the form (<i>p</i><sup><i>k</i></sup><i>, p</i><sup><i>k</i></sup><i>, c</i>), where <i>p</i><sup><i>k</i></sup> is a prime power. As a numerical application, we determine the complete list of values the degree of compositum <i>KL</i> can take if <i>K</i> and <i>L</i> are two number fields of degree 16.</p>

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Compositum of two number fields of prime power degree

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Paulius Virbalas

摘要

A triplet of positive integers (a, b, c) 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. In this paper, by applying the recently completed classification of almost simple groups of prime power degree, we discover previously unknown compositum-feasible triplets of the form (pk, pk, c), where pk is a prime power. As a numerical application, we determine the complete list of values the degree of compositum KL can take if K and L are two number fields of degree 16.