We discuss the problem of calculating generators of power integral bases in sextic fields, especially focusing on the case of sextic fields with real quadratic subfields. Our main purpose is to describe an efficient algorithm for calculating generators of power integral bases. We show that appropriately using integer arithmetics speeds up the calculations considerably. Our experiences lead to some interesting general statements on generators of power integral bases in number fields generated by a unit.

monogenity, power integral basis, sextic fields, relative cubic extension, quadratic subfield, relative Thue equations, sieving

Received: March 12, 2025; Revised: March 28, 2025; Accepted: April 8, 2025; Published: April 14, 2025

How to cite this article: István Gaál, Calculating generators of power integral bases in sextic fields with a real quadratic subfield, JP Journal of Algebra, Number Theory and Applications 64(3) (2025), 289-306. https://doi.org/10.17654/0972555525016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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