Primes of higher degree and annihilators of class groups. (English) Zbl 07796585
Summary: Let \(L/K\) be a Galois extension of number fields with Galois group \(G\). We discuss a new method, by studying primes of higher residue degree, to obtain elements in \(\mathbb{Z}[G]\) which annihilate the class group of \(L\). We illustrate the method by obtaining annihilators of class groups for some cyclotomic fields. We mention some results on factors of class numbers which can be obtained from the study of primes of higher degree. We also mention connections of this study to some classical questions to highlight importance of primes of higher residue degree.
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