Investigating Monogenity in a Family of Cyclic Sextic Fields

István Gaál ()
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István Gaál: Institute of Mathematics, University of Debrecen, H-4032 Debrecen, Hungary

Mathematics, 2025, vol. 13, issue 12, 1-8

Abstract: Jones characterized, among others, monogenity of a family of cyclic sextic polynomials. Our purpose is to study monogenity of the family of corresponding sextic number fields. We show that several of these number fields are monogenic, despite the defining polynomial of their generating element being non-monogenic. In the monogenic fields, there are several inequivalent generators of power integral bases. Our calculation also provides the first non-trivial application of the method described earlier to study monogenity in totally real extensions of imaginary quadratic fields, emphasizing the efficiency of that algorithm.

Keywords: monogenity; power integral basis; sextic fields; relative cubic extension; quadratic subfield; Thue equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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